Graphing Inequalities Example
•Download as PPTX, PDF•
0 likes•630 views
1) Graph the inequality x - 3y < -9 by changing it to an equality, x - 3y = -9, and graphing the line. 2) Plot the points (0,3) and (-9,0) where x and y equal 0. 3) Draw the line and shade the side that does not contain the point (0,0), which does not satisfy the original inequality of x - 3y < -9.
Report
Share
Report
Share
Recommended
Straight line-equation.
The document discusses straight line equations and graphs. It provides examples of finding the equation of a straight line from its graph by determining the gradient and y-intercept. It also shows how to calculate the gradient between two points and use it to find the equation of a line passing through two given points. Formulas for gradient and the equation of a line are reviewed.
Introduction to straight line graphs lesson
This document introduces straight line graphs by discussing drawing graphs from their equations, investigating different graphs, revising substitution, and plotting coordinates. It provides examples of linear equations like y = x + 7 and shows how to draw the line graph for y = 2x. The document discusses using substitution to replace x-values in an equation and plot the resulting y-values in order to draw the graph.
5.4 Slope Intercept Form Part B
The document provides examples and practice problems for writing equations of lines in slope-intercept form (y=mx+b) by given the slope and y-intercept or two points on the line. It demonstrates how to find the slope from two points, the y-intercept from the slope and a given point, and how to write the final equation. Multiple examples are worked through step-by-step for writing equations of lines from their graphs, slopes, y-intercepts and point pairs.
4.9 Graphing Quadratic Inequalities
Graphs of quadratic inequalities will be parabolas with solid or dotted lines and shaded regions above or below the parabola. To graph: 1) sketch the parabola y=ax^2+bx+c, 2) choose a test point and see if it satisfies the inequality, 3) shade the appropriate region based on the test point. For example, to graph y ≤ x^2+6x-4: the parabola opens up with a solid line and vertex at (-3,-13), the test point (0,0) satisfies the inequality so shade below the parabola.
5.7 Quadratic Inequalities
This document discusses how to graph and solve quadratic inequalities in one and two variables. It provides examples of graphing quadratic inequalities by drawing the parabola, choosing a test point, and shading the appropriate region. Systems of quadratic inequalities can be graphed on the same grid, with the shared shaded region representing the solutions. Quadratic inequalities in one variable can also be solved by graphing the parabola and identifying the x-values where it lies above or below the x-axis, or algebraically by solving the inequality as an equation and testing values between the solutions.
04 scaling analog_datal_sp17
A linear function is an equation that graphs as a straight line, with the general form of y = mx + b, where m is the slope and b is the y-intercept. A linear equation can be offset by changing the b term, which shifts the line up or down but does not change its slope. The slope of the line can be changed by multiplying the x term by a different value for m. Graphing linear equations with different slopes and offsets demonstrates how varying the terms affects the resulting line.
4 6 equations of lines
The document discusses equations of lines. It introduces the linear equation y = 2x - 1 and shows how to graph it by substituting values for x and finding the corresponding y-values. This forms the line's points (ordered pairs). It explains that a linear equation can be written in the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept. It provides examples of writing equations from their graphs in slope-intercept form and graphing lines from equations written in this form by using the slope and y-intercept. Finally, it gives examples of writing equations of lines parallel or perpendicular to given lines that pass through a given point.
Line Drawing Algorithms - Computer Graphics - Notes
Straight-line drawing algorithms are based on incremental methods.
In incremental method line starts with a straight point, then some fix incrementable is added to current point to get next point on the line and the same has continued all the end of the line.
Recommended
Straight line-equation.
The document discusses straight line equations and graphs. It provides examples of finding the equation of a straight line from its graph by determining the gradient and y-intercept. It also shows how to calculate the gradient between two points and use it to find the equation of a line passing through two given points. Formulas for gradient and the equation of a line are reviewed.
Introduction to straight line graphs lesson
This document introduces straight line graphs by discussing drawing graphs from their equations, investigating different graphs, revising substitution, and plotting coordinates. It provides examples of linear equations like y = x + 7 and shows how to draw the line graph for y = 2x. The document discusses using substitution to replace x-values in an equation and plot the resulting y-values in order to draw the graph.
5.4 Slope Intercept Form Part B
The document provides examples and practice problems for writing equations of lines in slope-intercept form (y=mx+b) by given the slope and y-intercept or two points on the line. It demonstrates how to find the slope from two points, the y-intercept from the slope and a given point, and how to write the final equation. Multiple examples are worked through step-by-step for writing equations of lines from their graphs, slopes, y-intercepts and point pairs.
4.9 Graphing Quadratic Inequalities
Graphs of quadratic inequalities will be parabolas with solid or dotted lines and shaded regions above or below the parabola. To graph: 1) sketch the parabola y=ax^2+bx+c, 2) choose a test point and see if it satisfies the inequality, 3) shade the appropriate region based on the test point. For example, to graph y ≤ x^2+6x-4: the parabola opens up with a solid line and vertex at (-3,-13), the test point (0,0) satisfies the inequality so shade below the parabola.
5.7 Quadratic Inequalities
This document discusses how to graph and solve quadratic inequalities in one and two variables. It provides examples of graphing quadratic inequalities by drawing the parabola, choosing a test point, and shading the appropriate region. Systems of quadratic inequalities can be graphed on the same grid, with the shared shaded region representing the solutions. Quadratic inequalities in one variable can also be solved by graphing the parabola and identifying the x-values where it lies above or below the x-axis, or algebraically by solving the inequality as an equation and testing values between the solutions.
04 scaling analog_datal_sp17
A linear function is an equation that graphs as a straight line, with the general form of y = mx + b, where m is the slope and b is the y-intercept. A linear equation can be offset by changing the b term, which shifts the line up or down but does not change its slope. The slope of the line can be changed by multiplying the x term by a different value for m. Graphing linear equations with different slopes and offsets demonstrates how varying the terms affects the resulting line.
4 6 equations of lines
The document discusses equations of lines. It introduces the linear equation y = 2x - 1 and shows how to graph it by substituting values for x and finding the corresponding y-values. This forms the line's points (ordered pairs). It explains that a linear equation can be written in the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept. It provides examples of writing equations from their graphs in slope-intercept form and graphing lines from equations written in this form by using the slope and y-intercept. Finally, it gives examples of writing equations of lines parallel or perpendicular to given lines that pass through a given point.
Line Drawing Algorithms - Computer Graphics - Notes
Straight-line drawing algorithms are based on incremental methods.
In incremental method line starts with a straight point, then some fix incrementable is added to current point to get next point on the line and the same has continued all the end of the line.
Creating Population Pyramids
This document provides a step-by-step guide to create a clustered bar graph in Excel. It includes instructions to enter formulas to calculate percentages based on data in columns C through E, copy and paste the formulas, cut and paste columns, and format a bar graph with an x-axis label, y-axis title, and chart title. The graph created compares the percentages of two calculations across categories in the x-axis.
Standard form solve equations
The document discusses standard form for linear equations and provides examples of converting equations to standard form. It also discusses writing equations of lines given different forms, including slope-intercept form, standard form, and point-slope form. Steps are provided for solving two-step equations by using the opposite operations to isolate the variable. Examples demonstrate converting equations to standard form, writing equations given the slope and y-intercept or two points, and solving a two-step equation.
March 8 Graphing Slope Intercept
The document discusses using the slope-intercept method to graph lines. It explains that the slope-intercept method involves finding a point on the line, such as the y-intercept, and using the slope to find another point. It then works through examples of graphing lines using this method, showing how to identify the slope and y-intercept from equations in slope-intercept form or standard form.
Straight line graphs
This document discusses straight line graphs and various methods for plotting straight lines on a graph. It covers identifying horizontal, vertical and diagonal lines, writing equations in y=mx+c form, using a table method to plot lines by substituting x-values, and using the x=0, y=0 method to find two points and plot a line from its equation. Exercises are provided for students to practice identifying and plotting different types of straight lines.
4 5 slope
The document discusses slope and how it can be used to help a pilot adjust their flight path to clear an obstacle like a mountain. It defines slope as the ratio of the rise (vertical change) over the run (horizontal change) between two points on a line. By communicating the required slope to the pilot, the person could tell them how much they need to change their altitude relative to the distance they need to travel horizontally in order to safely pass over the mountain without crashing into it.
Section 4.5 graphing linear equations
The document summarizes how to graph linear equations. It discusses:
1) The standard form of a linear equation is Ax + By = C, where A and B are integers with greatest common factor of 1.
2) Linear equations can also be written in y-intercept form as y = mx + b, where y has a coefficient of +1.
3) Examples are given of converting between standard and y-intercept form.
4) The document shows how to graph linear equations by plotting points in a table using the equation to relate x and y values.
Derivatives and slope 2.1 update day1
The document discusses how to identify tangent lines and find derivatives using limits. It defines the slope of a tangent line as the rate of change of a graph at a given point. To calculate slope, it uses the limit of the difference quotient as the change in x (Δx) approaches 0. This defines the derivative as the slope of the tangent line. It provides an example of finding the derivative of f(x)=x^2 at the point (2,4) using this limit process.
5.2 Define Slope
The document provides examples of calculating slope from graphs and points. It defines slope as "rise over run" and discusses identifying lines with positive, negative, or zero slopes from graphs. Several examples are given of calculating the slope of lines from their graphs or from two points on each line. Slopes are calculated using the formula: Slope = (y2 - y1) / (x2 - x1).
Quadratic functions
This document describes how to transform quadratic functions from general form to standard form in three steps:
1) Factor out the leading coefficient a from the first two terms.
2) Complete the square of the factored quadratic expression.
3) Factor the completed square and combine like terms.
Examples of transforming specific quadratic functions like f(x) = x^2 - 8x + 3 and f(x) = 2x^2 + 5x - 1 are provided. An activity with 5 quadratic functions to transform to standard form is listed at the end.
1.4.3 Slopes and Equations of Lines
The document discusses slopes and equations of lines. It defines slope as rise over run and explains how to calculate slope from two points on a line or from the graph of a line. It also explains how to write the equation of a line in point-slope form, slope-intercept form, or for horizontal and vertical lines. Several examples are provided of finding slopes and writing line equations in different forms.
Linear equation 2 2
The document discusses linear equations and their graphs. It explains how to write linear equations in standard form (Ax + By = C) and how to find the x-intercept and y-intercept of a linear equation by setting x or y equal to 0 and solving for the other variable. The x-intercept is where the graph crosses the x-axis and the y-intercept is where it crosses the y-axis. Some examples are worked through, including cases where there is no x-intercept for a horizontal line.
Assignment 1 b
This document contains a tutorial assignment with 3 questions for the subject Engineering Mathematics-III. Question 1 involves proving mathematical expressions and finding a missing term from a table. Question 2 involves using interpolation formulas like Newton Gregory and Newton forward/backward to find values from tables and calculate frequencies. Question 3 involves using Lagrange's and Newton divided difference formulas to find function values from data points in tables and determine maximum/minimum values.
A25-7 Quadratic Inequalities
This document provides instructions for graphing and solving quadratic inequalities. It explains how to graph parabolas defined by inequalities using a graphing calculator. It also describes how to graph systems of quadratic inequalities by first graphing the individual parabolas and then shading the overlapping regions indicated by the inequalities. When solving inequalities, it advises finding the critical values by setting the expression equal to zero and factoring, and then plotting these values on a number line to determine the solution intervals.
Graphing lines using slopeintercept
This document provides information about graphing lines using slope-intercept form. It defines slope-intercept form as y=mx+b, where m is the slope and b is the y-intercept. It shows how to find the slope and y-intercept from linear equations in various forms and how to write equations in slope-intercept form. It also demonstrates how to graph lines by plotting points using the slope and y-intercept. Key steps for graphing include finding the slope and y-intercept, plotting the y-intercept, using the slope to determine other points, and drawing the line through the points. The document also discusses parallel lines as those with the same slope.
Inequalities day 2 worked
This document discusses using sign charts to solve non-linear inequalities. Sign charts are used to determine the signs of expressions over intervals of x to identify possible solutions. Examples shown include using sign charts to solve inequalities like (3)1 0x x− + ≥, 2 3( 4) 0x x− < + 1, and 5 3 0x x+ < + − 3 1. Homework problems listed are from page 265 problems 33 through 54.
คาบ 5 7
This document discusses linear equations in two variables. It defines linear equations and explains how to find the slope of a line using the slope formula. It presents the slope-intercept form and point-slope forms of linear equations and how to graph lines using these forms. It also discusses parallel and perpendicular lines based on the slopes of the lines.
2 punto medio
This document demonstrates how to find the midpoint M(x,y) of points on a coordinate plane. It provides examples of finding the midpoints of points A(10,2) and B(20,24), which is M(15,13); of points R(-12,-8) and C(16,12), which is M(2,2); and of points F(-9,3) and F(12,-6), which is M(-3,1). It also shows working through examples of finding the x- and y-coordinates that satisfy midpoint equations.
Navigating the producer portal
Health insurance plans have deductibles that must be paid by the policyholder before insurance begins to cover healthcare costs. Deductibles are usually paid on an annual basis, so costs from late in one year do not carry over to the next. Meeting the deductible helps control insurance costs for everyone by reducing frequent small claims.
Vidyo helped REACH Health Effectively Handle Emergency Care
REACH Health is at the forefront of delivering patient care with telemedicine platform, especially in acute and emergency scenarios. Bringing expert healthcare teams and remote patients together for better interactions and healthcare workflow was a challenge.
Vidyo’s software based video conferencing capabilities was integrated into REACH telehealth system which allows physicians to connect with patients in no time. REACH Health is equipped with time immediate physician assistance possibility in the area of telestroke using Vidyo’s video conferencing platform.
More about Vidyo’s telemedicine solutions: http://www.vidyo.com/solutions/healthcare/
Healthiest You employer presentation
Over 70% of ER, urgent care, and doctor visits can be safely handled over the phone. The healthiestyou platform provides 24/7 access to licensed US doctors through phone, video, or email consultations to diagnose, prescribe medications, and provide medical advice for common conditions like allergies and bronchitis. It offers a personalized online wellness program and prescription drug price comparison tool to empower people to improve their health while potentially reducing costs. Member surveys found high rates of satisfaction and that issues were typically resolved in under 30 minutes through the telehealth service.
MIT HackingMedicine SXSW_howhackhealthcare_0314
MIT HackingMedicine SXSW_howhackhealthcare_0314Hacking Medicine, Massachusetts Institute of Technology
We held a half-day workshop on the philosophy, process and tools to convene healthcare hackathons to uncover and rapidly validate unmet needs in healthcare.MIT Digital Healthcare Conference
This document discusses an upcoming digital health conference hosted by MIT's Industrial Liaison Program. It outlines some of the challenges of early-stage medical ventures, including navigating healthcare complexity and prioritizing risks. The document also discusses techniques for scaling medicine using new technologies, examples of high-growth digital health companies, and analyzing venture capital opportunities in the healthcare field.
More Related Content
What's hot
Creating Population Pyramids
This document provides a step-by-step guide to create a clustered bar graph in Excel. It includes instructions to enter formulas to calculate percentages based on data in columns C through E, copy and paste the formulas, cut and paste columns, and format a bar graph with an x-axis label, y-axis title, and chart title. The graph created compares the percentages of two calculations across categories in the x-axis.
Standard form solve equations
The document discusses standard form for linear equations and provides examples of converting equations to standard form. It also discusses writing equations of lines given different forms, including slope-intercept form, standard form, and point-slope form. Steps are provided for solving two-step equations by using the opposite operations to isolate the variable. Examples demonstrate converting equations to standard form, writing equations given the slope and y-intercept or two points, and solving a two-step equation.
March 8 Graphing Slope Intercept
The document discusses using the slope-intercept method to graph lines. It explains that the slope-intercept method involves finding a point on the line, such as the y-intercept, and using the slope to find another point. It then works through examples of graphing lines using this method, showing how to identify the slope and y-intercept from equations in slope-intercept form or standard form.
Straight line graphs
This document discusses straight line graphs and various methods for plotting straight lines on a graph. It covers identifying horizontal, vertical and diagonal lines, writing equations in y=mx+c form, using a table method to plot lines by substituting x-values, and using the x=0, y=0 method to find two points and plot a line from its equation. Exercises are provided for students to practice identifying and plotting different types of straight lines.
4 5 slope
The document discusses slope and how it can be used to help a pilot adjust their flight path to clear an obstacle like a mountain. It defines slope as the ratio of the rise (vertical change) over the run (horizontal change) between two points on a line. By communicating the required slope to the pilot, the person could tell them how much they need to change their altitude relative to the distance they need to travel horizontally in order to safely pass over the mountain without crashing into it.
Section 4.5 graphing linear equations
The document summarizes how to graph linear equations. It discusses:
1) The standard form of a linear equation is Ax + By = C, where A and B are integers with greatest common factor of 1.
2) Linear equations can also be written in y-intercept form as y = mx + b, where y has a coefficient of +1.
3) Examples are given of converting between standard and y-intercept form.
4) The document shows how to graph linear equations by plotting points in a table using the equation to relate x and y values.
Derivatives and slope 2.1 update day1
The document discusses how to identify tangent lines and find derivatives using limits. It defines the slope of a tangent line as the rate of change of a graph at a given point. To calculate slope, it uses the limit of the difference quotient as the change in x (Δx) approaches 0. This defines the derivative as the slope of the tangent line. It provides an example of finding the derivative of f(x)=x^2 at the point (2,4) using this limit process.
5.2 Define Slope
The document provides examples of calculating slope from graphs and points. It defines slope as "rise over run" and discusses identifying lines with positive, negative, or zero slopes from graphs. Several examples are given of calculating the slope of lines from their graphs or from two points on each line. Slopes are calculated using the formula: Slope = (y2 - y1) / (x2 - x1).
Quadratic functions
This document describes how to transform quadratic functions from general form to standard form in three steps:
1) Factor out the leading coefficient a from the first two terms.
2) Complete the square of the factored quadratic expression.
3) Factor the completed square and combine like terms.
Examples of transforming specific quadratic functions like f(x) = x^2 - 8x + 3 and f(x) = 2x^2 + 5x - 1 are provided. An activity with 5 quadratic functions to transform to standard form is listed at the end.
1.4.3 Slopes and Equations of Lines
The document discusses slopes and equations of lines. It defines slope as rise over run and explains how to calculate slope from two points on a line or from the graph of a line. It also explains how to write the equation of a line in point-slope form, slope-intercept form, or for horizontal and vertical lines. Several examples are provided of finding slopes and writing line equations in different forms.
Linear equation 2 2
The document discusses linear equations and their graphs. It explains how to write linear equations in standard form (Ax + By = C) and how to find the x-intercept and y-intercept of a linear equation by setting x or y equal to 0 and solving for the other variable. The x-intercept is where the graph crosses the x-axis and the y-intercept is where it crosses the y-axis. Some examples are worked through, including cases where there is no x-intercept for a horizontal line.
Assignment 1 b
This document contains a tutorial assignment with 3 questions for the subject Engineering Mathematics-III. Question 1 involves proving mathematical expressions and finding a missing term from a table. Question 2 involves using interpolation formulas like Newton Gregory and Newton forward/backward to find values from tables and calculate frequencies. Question 3 involves using Lagrange's and Newton divided difference formulas to find function values from data points in tables and determine maximum/minimum values.
A25-7 Quadratic Inequalities
This document provides instructions for graphing and solving quadratic inequalities. It explains how to graph parabolas defined by inequalities using a graphing calculator. It also describes how to graph systems of quadratic inequalities by first graphing the individual parabolas and then shading the overlapping regions indicated by the inequalities. When solving inequalities, it advises finding the critical values by setting the expression equal to zero and factoring, and then plotting these values on a number line to determine the solution intervals.
Graphing lines using slopeintercept
This document provides information about graphing lines using slope-intercept form. It defines slope-intercept form as y=mx+b, where m is the slope and b is the y-intercept. It shows how to find the slope and y-intercept from linear equations in various forms and how to write equations in slope-intercept form. It also demonstrates how to graph lines by plotting points using the slope and y-intercept. Key steps for graphing include finding the slope and y-intercept, plotting the y-intercept, using the slope to determine other points, and drawing the line through the points. The document also discusses parallel lines as those with the same slope.
Inequalities day 2 worked
This document discusses using sign charts to solve non-linear inequalities. Sign charts are used to determine the signs of expressions over intervals of x to identify possible solutions. Examples shown include using sign charts to solve inequalities like (3)1 0x x− + ≥, 2 3( 4) 0x x− < + 1, and 5 3 0x x+ < + − 3 1. Homework problems listed are from page 265 problems 33 through 54.
คาบ 5 7
This document discusses linear equations in two variables. It defines linear equations and explains how to find the slope of a line using the slope formula. It presents the slope-intercept form and point-slope forms of linear equations and how to graph lines using these forms. It also discusses parallel and perpendicular lines based on the slopes of the lines.
2 punto medio
This document demonstrates how to find the midpoint M(x,y) of points on a coordinate plane. It provides examples of finding the midpoints of points A(10,2) and B(20,24), which is M(15,13); of points R(-12,-8) and C(16,12), which is M(2,2); and of points F(-9,3) and F(12,-6), which is M(-3,1). It also shows working through examples of finding the x- and y-coordinates that satisfy midpoint equations.
What's hot (17)
Viewers also liked
Navigating the producer portal
Health insurance plans have deductibles that must be paid by the policyholder before insurance begins to cover healthcare costs. Deductibles are usually paid on an annual basis, so costs from late in one year do not carry over to the next. Meeting the deductible helps control insurance costs for everyone by reducing frequent small claims.
Vidyo helped REACH Health Effectively Handle Emergency Care
REACH Health is at the forefront of delivering patient care with telemedicine platform, especially in acute and emergency scenarios. Bringing expert healthcare teams and remote patients together for better interactions and healthcare workflow was a challenge.
Vidyo’s software based video conferencing capabilities was integrated into REACH telehealth system which allows physicians to connect with patients in no time. REACH Health is equipped with time immediate physician assistance possibility in the area of telestroke using Vidyo’s video conferencing platform.
More about Vidyo’s telemedicine solutions: http://www.vidyo.com/solutions/healthcare/
Healthiest You employer presentation
Over 70% of ER, urgent care, and doctor visits can be safely handled over the phone. The healthiestyou platform provides 24/7 access to licensed US doctors through phone, video, or email consultations to diagnose, prescribe medications, and provide medical advice for common conditions like allergies and bronchitis. It offers a personalized online wellness program and prescription drug price comparison tool to empower people to improve their health while potentially reducing costs. Member surveys found high rates of satisfaction and that issues were typically resolved in under 30 minutes through the telehealth service.
MIT HackingMedicine SXSW_howhackhealthcare_0314
MIT HackingMedicine SXSW_howhackhealthcare_0314Hacking Medicine, Massachusetts Institute of Technology
We held a half-day workshop on the philosophy, process and tools to convene healthcare hackathons to uncover and rapidly validate unmet needs in healthcare.MIT Digital Healthcare Conference
This document discusses an upcoming digital health conference hosted by MIT's Industrial Liaison Program. It outlines some of the challenges of early-stage medical ventures, including navigating healthcare complexity and prioritizing risks. The document also discusses techniques for scaling medicine using new technologies, examples of high-growth digital health companies, and analyzing venture capital opportunities in the healthcare field.
MIT Hacking Medicine Institute - Genomics Adventures 2.0
MIT Hacking Medicine Institute - Genomics Adventures 2.0Hacking Medicine, Massachusetts Institute of Technology
The document discusses several challenges and opportunities in the genomics field, including issues scaling genomic data analysis, tensions around data sharing, and the massive costs required for patient awareness and activation. It also profiles two leaders in the genomics space, highlighting their backgrounds and roles in advising on precision medicine opportunities and investments.Armens TD_Sales_Presentation
This document provides information about Teladoc, a telehealth and virtual healthcare services company. It highlights Teladoc's industry leadership position, the various care options and clinical specialties it provides, positive patient satisfaction and client retention rates, and examples of cost savings and utilization increases experienced by its clients. The document also describes Teladoc's user-friendly virtual care platform and mobile app, its focus on client success and marketing support, and pricing information for its telehealth services.
Digital Health Minimum Viable Products MIT_healthcare_ventures_2015
Digital Health Minimum Viable Products MIT_healthcare_ventures_2015Hacking Medicine, Massachusetts Institute of Technology
This document discusses minimum viable products (MVPs) and their application to early stage medical ventures. It begins by outlining the MVP design process of observing user needs, pitching initial designs, testing prototypes, and learning from feedback to iterate the product. The document emphasizes validating problems and solutions quickly through experiments and metrics rather than assumptions. Examples are provided of digital health MVPs like PillPack's paper prototyping and Figure 1's crowdsourced medical image database. The document stresses focusing MVPs on the fastest path to return on investment by prioritizing risks upfront. It advocates spending equal time on product development and customer traction testing to achieve product-market fit. Overall, the document promotes applying lean startup principles ofLean Startup for Healthcare: Workshop at Healthbox
This document discusses how to use Lean Startup principles and practices to innovate healthcare products faster. It introduces Lean Startup, which focuses on rapidly testing assumptions and reducing risks through customer feedback. Key aspects covered include building minimum viable products (MVPs), conducting problem and solution interviews, and the goal of achieving product-market fit by increasing customer lifetime value and decreasing customer acquisition costs after launching. The document provides an overview of the Lean Startup process and emphasizes getting customer input early through various validation techniques.
Tracxn Research - Telemedicine Landscape Report, August 2016
The document is a telemedicine report from August 2016 by Tracxn, which tracks startups and deals. It provides an overview of telemedicine sectors including tele-consultation, tele-monitoring, tech enablers and tele-rehabilitation. Key highlights from the report include:
- Tele-consultation received the most funding ($2.1B), followed by tele-monitoring ($424M) and tech enablers ($169M).
- The top funded companies in each sector are Ping An Good Doctor and Chunyu Yisheng in tele-consultation, iRhythm Tech in tele-monitoring, and InTouch Technologies in tech enablers.
- Most active investors in
Viewers also liked (10)
Vidyo helped REACH Health Effectively Handle Emergency Care
Vidyo helped REACH Health Effectively Handle Emergency Care
MIT Hacking Medicine Institute - Genomics Adventures 2.0
MIT Hacking Medicine Institute - Genomics Adventures 2.0
Digital Health Minimum Viable Products MIT_healthcare_ventures_2015
Digital Health Minimum Viable Products MIT_healthcare_ventures_2015
Lean Startup for Healthcare: Workshop at Healthbox
Lean Startup for Healthcare: Workshop at Healthbox
Tracxn Research - Telemedicine Landscape Report, August 2016
Tracxn Research - Telemedicine Landscape Report, August 2016
Similar to Graphing Inequalities Example
CST 504 Graphing Inequalities
This document provides instructions for graphing inequalities on a coordinate plane. It begins by graphing examples of inequalities on a number line and plane. It then explains how to graph linear inequalities by writing them as equations, making a table of x-y values, plotting the points, and drawing the boundary line. Examples are provided of graphing inequalities in slope-intercept form such as y ≥ -3x + 2. The document also covers testing points, determining whether to shade above or below the line, and applying the process to graph more complex inequalities like 3x - 4y > 12. It concludes with an example of using inequalities to model real-world constraints and find maximum/minimum values through optimization
February 3, 2015
The document contains notes and examples about graphing linear inequalities on a coordinate plane. It discusses writing inequalities in y=mx+b form, determining the boundary line, and shading the appropriate region based on whether the inequality is <, ≤, >, or ≥. Key steps include solving the inequality for y, graphing the boundary line, and testing a point such as (0,0) to determine which side of the line to shade.
Linear equations 2-2 a graphing and x-y intercepts
The document provides information about graphing points and linear equations on the Cartesian coordinate plane. It defines key terms like ordered pairs, x- and y-intercepts, and quadrants. It explains how to graph linear equations by finding x- and y-intercepts or substituting values into the equation to find points. Horizontal and vertical lines are identified, with their equations using either a constant x or y value.
2 3 Bzca5e
The document discusses linear functions and slopes. It provides examples of finding the slope of a line between two points, writing the equation of a line in point-slope and slope-intercept form, graphing linear equations, finding the x- and y-intercepts of a line, and applications of linear functions including using a graphing calculator.
January 27, 2014
The document contains notes about Khan Academy assignments being due, exam grades being posted, and notebooks being collected on different days of the week. It also includes examples of writing inequalities, graphing linear inequalities, and solving word problems involving inequalities describing the number of coins a person could have with less than $5.
February 18 2016
The document discusses various formulas used to represent lines in the coordinate plane, including:
- Slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept.
- Point-slope form: y – y1 = m(x – x1), where (x1, y1) is a known point on the line and m is the slope.
- Standard form: Ax + By = C, where A, B, and C are constants and A and B cannot both be 0.
It provides examples of writing equations of lines in different forms given information like the slope, a point, or the graph of the line. Converting between
January 11
1) The document discusses graphing linear inequalities on a number line and coordinate plane. It provides examples of solving inequalities for y and graphing the corresponding boundary lines, shading the appropriate regions.
2) Methods for graphing inequalities include solving for y, graphing the boundary line, and shading the correct region based on whether the inequality is <, ≤, >, or ≥.
3) An example problem models an inequality describing the maximum number of nickels and dimes that can be had with less than $5.00, graphing the solution on the n-d plane.
Quadratic equations
This document discusses quadratic equations and methods for solving them. It begins by defining quadratic equations as second degree polynomial equations of the form ax^2 + bx + c = 0, where a is not equal to 0. It then presents several methods for finding the roots or solutions of quadratic equations: factoring, completing the square, and using the quadratic formula. Examples are provided to illustrate each method. The document also discusses graphing quadratic functions and key features of parabolas such as vertex, axis of symmetry, and direction of opening.
WCS Specialist Maths An Introduction to Matrices PowerPoint
Matrices are tables of numbers arranged in rows and columns. They can be used to store and organize data, simplify mathematical functions, and solve simultaneous equations. To multiply matrices, the numbers in corresponding positions are multiplied and summed. The determinant of a matrix is a single number that defines the matrix. Inverting a matrix allows it to be used to solve simultaneous equations in matrix form. Larger matrices use more complex rules and calculations for operations like determining the determinant and inverse.
WRITING AND GRAPHING LINEAR EQUATIONS 1.pptx
The document discusses linear equations and graphing linear relationships. It defines key terms like slope, y-intercept, x-intercept, and provides examples of writing linear equations in slope-intercept form and point-slope form given certain information like a point and slope. It also discusses using tables and graphs to plot linear equations and find slopes from graphs or between two points. Real-world examples of linear relationships are provided as well.
Função quadrática
The document is about quadratic polynomial functions and contains the following information:
1. It discusses investigating relationships between numbers expressed in tables to represent them in the Cartesian plane, identifying patterns and creating conjectures to generalize and algebraically express this generalization, recognizing when this representation is a quadratic polynomial function of the type y = ax^2.
2. It provides examples of converting algebraic representations of quadratic polynomial functions into geometric representations in the Cartesian plane, distinguishing cases in which one variable is directly proportional to the square of the other, using or not using software or dynamic algebra and geometry applications.
3. It discusses characterizing the coefficients of quadratic functions, constructing their graphs in the Cartesian plane, and determining their zeros (
PPT 6.8 Graphing Linear Inequalities.ppt
1. Solve the inequality for y: y > 2x - 3.5
2. Graph the boundary line y = 2x - 3.5 as a solid line since the inequality symbol is <
3. Test a point, such as the origin (0,0), which satisfies the inequality so shade below the boundary line where the solutions lie.
PPT 6.8 Graphing Linear Inequalities.ppt
1) Solve the inequality for y to get y > 2x - 3.5 and graph the boundary line y = 2x - 3.5 as a solid line. 2) Since the inequality symbol is <, shade below the boundary line where the solutions lie. 3) Check a point not on the line, like (0,0), to verify it does not satisfy the inequality and confirm the shading is below the boundary line.
C2 st lecture 2 handout
This document provides a summary of lecture 2 on quadratic equations and straight lines. It covers how to factorize, complete the square, and use the quadratic formula to solve quadratic equations. It also discusses how to find the equation of a straight line given its gradient and y-intercept, or two points on the line. Additionally, it explains how to sketch lines, find the midpoint and distance between two points. Key terms defined include quadratic, surd, gradient, and intercept. Methods demonstrated include solving quadratic equations, finding lines from gradient/point and two points, and calculating midpoints and distances on a graph.
คาบ2 2
The document provides instructions for writing and graphing linear equations in slope-intercept form (y = mx + b). It defines key terms like slope (m), y-intercept (b), and parallel lines. Examples are given for writing equations from slope and y-intercept, graphing lines on a coordinate plane, and determining if two lines are parallel based on having the same slope. Key steps are outlined for graphing a line passing through a given point with a given slope.
Graphing Linear Inequalities
This document provides instructions for graphing linear inequalities by:
1) Finding the slope and y-intercept of the linear equation;
2) Plotting the line on the coordinate plane;
3) Testing a sample point to determine which half-plane to shade based on whether it satisfies the given inequality.
7 1solve By Graphing
This document introduces different methods for solving systems of linear equations: graphing, substitution, and elimination. It provides examples of solving systems by graphing them on a coordinate plane and finding the point of intersection. It also gives examples of converting equations between standard and slope-intercept form and using substitution and elimination to solve systems algebraically.
lect.no.3.pptx
The document discusses various topics related to graphics and plotting in MATLAB including: the plot command for creating 2D and 3D plots; options for specifying line styles; using linspace to generate uniformly spaced vectors; adding labels, titles, and text to figures; displaying data using plots, stem plots, bar charts; and including multiple graphs in the same figure. Key graphing functions covered are plot, stem, bar, title, xlabel, ylabel, text, and linspace. The document also includes examples of MATLAB code for generating various types of graphs and annotating them.
1538 graphs & linear equations
Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics
5.2 using intercepts
This document provides examples and explanations for finding the x- and y-intercepts of linear equations and using intercepts to graph lines. It defines x- and y-intercepts, shows how to find them by setting x or y equal to 0, and explains that intercepts represent important values on the graph like when distance or time is 0. Examples demonstrate finding intercepts, generating points, and graphing lines based on the intercepts.
Similar to Graphing Inequalities Example (20)
Linear equations 2-2 a graphing and x-y intercepts
Linear equations 2-2 a graphing and x-y intercepts
WCS Specialist Maths An Introduction to Matrices PowerPoint
WCS Specialist Maths An Introduction to Matrices PowerPoint
More from sbishoptcl
NSO Student Handbook
The student handbook provides information on policies such as attendance, calculating GPA, repeating courses, and changing majors. It can be found in PDF format on the college's website. The attendance policy requires students to attend 90% of classes and allows instructors to withdraw students who miss more than 10% of classes. The GPA is calculated by dividing the total quality points earned by the total credit hours, with each letter grade assigned a different number of quality points. When repeating a course, only the most recent grade is used in the GPA calculation. To change majors, a student must submit a change of major form and meet with their new academic advisor.
Information Literacy Orientation (Fall, 2012)
This document provides an overview of the research process and importance of evaluating information sources. It discusses the steps of identifying an information need, developing a topic using background information, creating a research strategy with keywords, finding information using the library catalog, databases and evaluating sources. The research process involves finding reliable information from trustworthy sources and avoiding inaccurate information online. Evaluating sources includes considering the author's credentials, accuracy of information and date of publication.
Powerpoint practice
This document discusses practicing with Powerpoint. Powerpoint is a popular presentation software used to create slideshows, presentations, reports and other documents. The document likely provides tips, tricks or lessons for using Powerpoint's various features to create effective presentations.
Information Literacy Orientation (Fall, 2011)
The document provides an overview of information literacy and the research process. It discusses the importance of evaluating information sources and outlines six steps for conducting research: 1) identifying information needs, 2) developing a topic using background information, 3) developing a research strategy, 4) finding and evaluating information, 5) writing and revising papers, and 6) documenting sources. The document also summarizes resources available at the local community college library such as books, databases, ebooks, and assistance from librarians.
Information Literacy Orientation
The document provides an overview of the research process and importance of information literacy. It discusses identifying an information need, developing a topic using background information, creating a research strategy with keywords, finding and evaluating information using the library catalog, databases, and other sources, writing and revising a paper, and properly documenting sources to avoid plagiarism. Steps in the research process include determining information needs, developing a topic, creating a search strategy, finding information, writing a paper, and citing sources.
Information Literacy Orientation
The document provides an overview of information literacy and the research process. It discusses the importance of finding reliable information from trustworthy sources and evaluating information critically. A six-step research process is outlined that involves identifying information needs, developing topics, creating search strategies, finding information, writing and revising papers, and properly citing sources to avoid plagiarism. Resources for conducting research at the library such as books, eBooks, databases, and librarians are also described.
More from sbishoptcl (6)
Recently uploaded
clinical examination of hip joint (1).pdf
described clinical examination all orthopeadic conditions .
DRUGS AND ITS classification slide share
Any substance (other than food) that is used to prevent, diagnose, treat, or relieve symptoms of a
disease or abnormal condition
A Survey of Techniques for Maximizing LLM Performance.pptx
A Survey of Techniques for Maximizing LLM Performance
Main Java[All of the Base Concepts}.docx
This is part 1 of my Java Learning Journey. This Contains Custom methods, classes, constructors, packages, multithreading , try- catch block, finally block and more.
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
Denis is a dynamic and results-driven Chief Information Officer (CIO) with a distinguished career spanning information systems analysis and technical project management. With a proven track record of spearheading the design and delivery of cutting-edge Information Management solutions, he has consistently elevated business operations, streamlined reporting functions, and maximized process efficiency.
Certified as an ISO/IEC 27001: Information Security Management Systems (ISMS) Lead Implementer, Data Protection Officer, and Cyber Risks Analyst, Denis brings a heightened focus on data security, privacy, and cyber resilience to every endeavor.
His expertise extends across a diverse spectrum of reporting, database, and web development applications, underpinned by an exceptional grasp of data storage and virtualization technologies. His proficiency in application testing, database administration, and data cleansing ensures seamless execution of complex projects.
What sets Denis apart is his comprehensive understanding of Business and Systems Analysis technologies, honed through involvement in all phases of the Software Development Lifecycle (SDLC). From meticulous requirements gathering to precise analysis, innovative design, rigorous development, thorough testing, and successful implementation, he has consistently delivered exceptional results.
Throughout his career, he has taken on multifaceted roles, from leading technical project management teams to owning solutions that drive operational excellence. His conscientious and proactive approach is unwavering, whether he is working independently or collaboratively within a team. His ability to connect with colleagues on a personal level underscores his commitment to fostering a harmonious and productive workplace environment.
Date: May 29, 2024
Tags: Information Security, ISO/IEC 27001, ISO/IEC 42001, Artificial Intelligence, GDPR
-------------------------------------------------------------------------------
Find out more about ISO training and certification services
Training: ISO/IEC 27001 Information Security Management System - EN | PECB
ISO/IEC 42001 Artificial Intelligence Management System - EN | PECB
General Data Protection Regulation (GDPR) - Training Courses - EN | PECB
Webinars: https://pecb.com/webinars
Article: https://pecb.com/article
-------------------------------------------------------------------------------
For more information about PECB:
Website: https://pecb.com/
LinkedIn: https://www.linkedin.com/company/pecb/
Facebook: https://www.facebook.com/PECBInternational/
Slideshare: http://www.slideshare.net/PECBCERTIFICATION
Types of Herbal Cosmetics its standardization.
Physiology and chemistry of skin and pigmentation, hairs, scalp, lips and nail, Cleansing cream, Lotions, Face powders, Face packs, Lipsticks, Bath products, soaps and baby product,
Preparation and standardization of the following : Tonic, Bleaches, Dentifrices and Mouth washes & Tooth Pastes, Cosmetics for Nails.
CACJapan - GROUP Presentation 1- Wk 4.pdf
Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
How to Manage Your Lost Opportunities in Odoo 17 CRM
Odoo 17 CRM allows us to track why we lose sales opportunities with "Lost Reasons." This helps analyze our sales process and identify areas for improvement. Here's how to configure lost reasons in Odoo 17 CRM
Advanced Java[Extra Concepts, Not Difficult].docx
This is part 2 of my Java Learning Journey. This contains Hashing, ArrayList, LinkedList, Date and Time Classes, Calendar Class and more.
Assessment and Planning in Educational technology.pptx
In an education system, it is understood that assessment is only for the students, but on the other hand, the Assessment of teachers is also an important aspect of the education system that ensures teachers are providing high-quality instruction to students. The assessment process can be used to provide feedback and support for professional development, to inform decisions about teacher retention or promotion, or to evaluate teacher effectiveness for accountability purposes.
Azure Interview Questions and Answers PDF By ScholarHat
Azure Interview Questions and Answers PDF By ScholarHat
The simplified electron and muon model, Oscillating Spacetime: The Foundation...
Discover the Simplified Electron and Muon Model: A New Wave-Based Approach to Understanding Particles delves into a groundbreaking theory that presents electrons and muons as rotating soliton waves within oscillating spacetime. Geared towards students, researchers, and science buffs, this book breaks down complex ideas into simple explanations. It covers topics such as electron waves, temporal dynamics, and the implications of this model on particle physics. With clear illustrations and easy-to-follow explanations, readers will gain a new outlook on the universe's fundamental nature.
RPMS TEMPLATE FOR SCHOOL YEAR 2023-2024 FOR TEACHER 1 TO TEACHER 3
RPMS Template 2023-2024 by: Irene S. Rueco
Introduction to AI for Nonprofits with Tapp Network
Dive into the world of AI! Experts Jon Hill and Tareq Monaur will guide you through AI's role in enhancing nonprofit websites and basic marketing strategies, making it easy to understand and apply.
How to Build a Module in Odoo 17 Using the Scaffold Method
Odoo provides an option for creating a module by using a single line command. By using this command the user can make a whole structure of a module. It is very easy for a beginner to make a module. There is no need to make each file manually. This slide will show how to create a module using the scaffold method.
Recently uploaded (20)
A Survey of Techniques for Maximizing LLM Performance.pptx
A Survey of Techniques for Maximizing LLM Performance.pptx
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
Film vocab for eal 3 students: Australia the movie
Film vocab for eal 3 students: Australia the movie
How to Manage Your Lost Opportunities in Odoo 17 CRM
How to Manage Your Lost Opportunities in Odoo 17 CRM
Assessment and Planning in Educational technology.pptx
Assessment and Planning in Educational technology.pptx
Azure Interview Questions and Answers PDF By ScholarHat
Azure Interview Questions and Answers PDF By ScholarHat
The simplified electron and muon model, Oscillating Spacetime: The Foundation...
The simplified electron and muon model, Oscillating Spacetime: The Foundation...
RPMS TEMPLATE FOR SCHOOL YEAR 2023-2024 FOR TEACHER 1 TO TEACHER 3
RPMS TEMPLATE FOR SCHOOL YEAR 2023-2024 FOR TEACHER 1 TO TEACHER 3
Introduction to AI for Nonprofits with Tapp Network
Introduction to AI for Nonprofits with Tapp Network
How to Build a Module in Odoo 17 Using the Scaffold Method
How to Build a Module in Odoo 17 Using the Scaffold Method
Graphing Inequalities Example
- 2. Example: Graph the inequality x – 3y < - 9 Step 1: Change the inequality sign (<) to an equality sign(=): x – 3y = -9 (This graphs the line)
- 3. Step 2: Set x = 0 and solve for y: x – 3y = -9 0 – 3y = -9 (x = 0 on the y-axis.) -3y = -9 -3 -3 y = 3 Plot the point (0,3)
- 4. -x x -y y 3 Plot the point (0,3)
- 5. Step 3: Set y = 0 and solve for x: x – 3y = - 9 x –3(0) = -9 (y = 0 on the x-axis.) x = -9 Plot the point (-9,0)
- 6. Step 4: Graph the line < > broken line ------------- y -x -y x -9 3
- 7. Step 5: Which side do I shade? Choose (0,0), as a test point, if it does not lie on the graph of the line. Substitute (0,0) for (x, y) in the inequality. x – 3y < - 9 0 – 3(0) < - 9 Is 0 < -9? No.
- 8. 0 is not less than -9 Do not shade the side of the line that contains the point (0,0). Shade the other side. x-x -y 3