Nov 17 Slope
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DMCIThe document defines slope as the steepness and direction of a line, calculated as the rise over the run or change in y over the change in x between two points on the line. It provides examples of calculating the slope between two points and finding the y-value of a third point given the slope. It also describes how the sign of the slope indicates whether a line is diagonal left, horizontal, or diagonal right and whether the slope is undefined if the line is vertical.
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Slope of a line
The document discusses slope and how to calculate it. It defines slope as the steepness of a line or the rate of change between two points. Slope is represented by the letter m. There are three main ways to calculate slope: 1) using the formula m = (y2 - y1) / (x2 - x1) for two points (x1, y1) and (x2, y2); 2) by finding the rise over run when given a graph; 3) by taking the coefficient of x when a line equation is in the form of y = mx + b, where m represents the slope. Examples are provided to demonstrate calculating slope using these different methods.
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The gradient of a line measures how steep the line is, and can be positive, negative, or zero. The gradient is calculated by taking the change in y over the change in x between two points on the line. If the line is vertical, its gradient cannot be determined. Examples are provided to demonstrate calculating the gradient using points on a line and the formula for change in y over change in x.
Classroom Assignment
This document discusses slope and rates of change. It defines slope as a measurement of a line's steepness, which is the ratio of rise over run. It provides examples of determining whether slopes are positive or negative and calculating slope given points on a line. The document also explains that a constant rate of change results in a linear graph, while a variable rate of change results in a nonlinear graph. Students are asked to create a poem and illustration about the rise over run relationship to slope.
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This document provides an overview of slope and how it is calculated and represented in algebra. It defines slope as rise over run and shows how to calculate it by counting squares between two points on a graph. Positive and negative slopes are introduced, as well as the slope-intercept form of a line, y=mx+b, where m is the slope and b is the y-intercept. Examples are given of calculating slope from points and graphing lines in slope-intercept form. Requirements for using the point-slope form, y-y1=m(x-x1), are also outlined.
Linear function and slopes of a line
This document provides an overview of linear functions and equations. It defines linear equations as having the standard form Ax + By = C, with examples and how to identify linear vs. nonlinear equations. Linear functions are defined as having the form f(x) = mx + b. The document discusses slope, x-intercepts, y-intercepts, and how to graph linear equations from these components. It also covers representing linear functions in slope-intercept form as y = mx + b, and point-slope form as y - y1 = m(x - x1).
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This document discusses linear equations in the form y=mx+b. It defines slope as rise over run, and the y-intercept as the point where the line crosses the y-axis. It provides examples of special lines with undefined or zero slopes. It explains how to find the equation of a line given two points, given slope and a point, or given just the slope and y-intercept. It also notes how to graph lines by starting at the y-intercept and moving up the rise and over the run.
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The document discusses slope and how to calculate it. It defines slope as the steepness of a line or the rate of change between two points. Slope is represented by the letter m. There are three main ways to calculate slope: 1) using the formula m = (y2 - y1) / (x2 - x1) for two points (x1, y1) and (x2, y2); 2) by finding the rise over run when given a graph; 3) by taking the coefficient of x when a line equation is in the form of y = mx + b, where m represents the slope. Examples are provided to demonstrate calculating slope using these different methods.
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This document discusses slope and rates of change. It defines slope as a measurement of a line's steepness, which is the ratio of rise over run. It provides examples of determining whether slopes are positive or negative and calculating slope given points on a line. The document also explains that a constant rate of change results in a linear graph, while a variable rate of change results in a nonlinear graph. Students are asked to create a poem and illustration about the rise over run relationship to slope.
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This document discusses linear equations in the form y=mx+b. It defines slope as rise over run, and the y-intercept as the point where the line crosses the y-axis. It provides examples of special lines with undefined or zero slopes. It explains how to find the equation of a line given two points, given slope and a point, or given just the slope and y-intercept. It also notes how to graph lines by starting at the y-intercept and moving up the rise and over the run.
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1. The document defines translations and reflections as geometric transformations. It provides examples of translating points by vectors and reflecting points across lines like the x-axis or y-axis.
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This document discusses finding slope and rate of change from examples. It provides examples of calculating slope from points on a line and determining if a line rises, falls, is horizontal, or vertical without graphing. It also discusses how to determine if two lines are parallel or perpendicular using their slopes, and gives an example of calculating rate of change to predict a percentage in 2005 based on past data points.
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The document discusses different forms and methods for graphing linear functions, including:
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2) Converting between these forms by solving for slope and y-intercept.
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4) Determining if two functions are parallel or perpendicular based on having equal or reciprocal slopes.
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This document contains a lesson on slope of a line from a mathematics course. It includes examples of calculating slope given two points on a line, identifying whether graphs represent constant or variable rates of change, and word problems applying slope to real-world contexts like cost of fruit and gas. The key points are that slope is defined as the ratio of rise over run, or change in y over change in x, and represents the constant rate of change for linear equations and functions.
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The slope of the line is 2. This is found by taking the change in y over the change in x between any two points. For example, between (0,0) and (1,2), the change in y is 2 and the change in x is 1, so the slope is 2/1 = 2.
Any linear equation can be written in the form y = mx + b, where m is the slope and b is the y-intercept (the y value when x is 0). Plugging in the points given, we can see that b must be 0. Therefore, the linear equation that fits the data is y = 2x.
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2. The slope of a line measures its steepness and is calculated using the slope formula.
3. Linear equations can be written in slope-intercept form y = mx + b or point-slope form y - y1 = m(x - x1) to graph the line.
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The document discusses slopes and equations of lines. It defines slope as the ratio of the rise to the run between two points on a line. It explains how to find the slope from two points, a graph, or an equation. It also explains how to write the equation of a line in point-slope form, slope-intercept form, or for horizontal and vertical lines. Examples are provided for finding slopes and writing equations in different forms.
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This document defines slope and provides examples for teaching students about slope. It explains that slope is the ratio of vertical to horizontal change and can be positive, negative, zero, or undefined. The objectives are for students to identify slope from graphs, calculate slope using rise over run, and apply the slope formula to find slope given two points. Examples are provided to demonstrate calculating slope from graphs and points using rise over run and the slope formula.
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1. The document discusses slope and rate of change, including how to calculate slope from two points on a line and how to interpret positive, negative, zero, and undefined slopes.
2. It provides examples of finding the slope of lines from graphs and points, and discusses how to identify parallel and perpendicular lines based on their slopes.
3. The key concepts are how to determine the steepness of a line from its slope, and that parallel lines have the same slope while perpendicular lines have slopes that are opposite reciprocals.
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The document provides information about linear equations and their graphs. It defines linear equations and discusses how to write equations in slope-intercept form, point-slope form, and standard form. It also describes how to graph linear equations by plotting intercepts and using slope. Key topics covered include finding the slope between two points, determining if lines are parallel or perpendicular based on their slopes, and recognizing the intercepts on a graph of a linear equation in two variables.
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This document discusses finding slope and rate of change from examples. It provides examples of calculating slope from points on a line and determining if a line rises, falls, is horizontal, or vertical without graphing. It also discusses how to determine if two lines are parallel or perpendicular using their slopes, and gives an example of calculating rate of change to predict a percentage in 2005 based on past data points.
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1) The standard, point-slope, and slope-intercept forms of linear equations.
2) Converting between these forms by solving for slope and y-intercept.
3) Graphing linear functions by finding the slope from two points using the point-slope form, making a table of x-y values, or finding the x- and y-intercepts.
4) Determining if two functions are parallel or perpendicular based on having equal or reciprocal slopes.
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This document contains a lesson on slope of a line from a mathematics course. It includes examples of calculating slope given two points on a line, identifying whether graphs represent constant or variable rates of change, and word problems applying slope to real-world contexts like cost of fruit and gas. The key points are that slope is defined as the ratio of rise over run, or change in y over change in x, and represents the constant rate of change for linear equations and functions.
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This document provides 21 examples of linear functions presented as both tables and graphs. Each example shows a linear function in slope-intercept form with different characteristics for the slope and y-intercept, such as positive and negative slopes greater than, less than, and equal to 1, as well as zero slopes and various y-intercepts. The examples cover a range of linear functions demonstrated visually and numerically.
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The linear equation for the line is y = 2x
The slope of the line is 2. This is found by taking the change in y over the change in x between any two points. For example, between (0,0) and (1,2), the change in y is 2 and the change in x is 1, so the slope is 2/1 = 2.
Any linear equation can be written in the form y = mx + b, where m is the slope and b is the y-intercept (the y value when x is 0). Plugging in the points given, we can see that b must be 0. Therefore, the linear equation that fits the data is y = 2x.
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This document discusses key concepts related to linear equations in two variables including:
1. Linear equations can be written in the form ax + by = c and are graphed as lines.
2. The slope of a line measures its steepness and is calculated using the slope formula.
3. Linear equations can be written in slope-intercept form y = mx + b or point-slope form y - y1 = m(x - x1) to graph the line.
4. Parallel lines have the same slope while perpendicular lines have slopes that are negative reciprocals.
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11X1 T08 03 angle between two lines (2010)
The document discusses how to find the acute angle between two lines with given slopes. It provides the formula for calculating the tangent of the acute angle (tan α) using the slopes (m1 and m2) of the two lines. Several examples are worked through step-by-step to demonstrate how to apply the formula to find the acute angle between two lines with specific slope values.
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for download this slide message me on gmail account techhubsolution0@gmail.com
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- Graphs are data structures consisting of nodes and edges connecting nodes.
- Examples of directed and undirected graphs are given.
- Graphs can be represented using adjacency matrices or adjacency lists. Adjacency matrices store connections in a grid and adjacency lists store connections as linked lists.
- Key graph terms are defined such as vertices, edges, paths, and degrees. Properties like connectivity and completeness are also discussed.
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The document discusses slopes and equations of lines. It defines slope as the ratio of the rise to the run between two points on a line. It explains how to find the slope from two points, a graph, or an equation. It also explains how to write the equation of a line in point-slope form, slope-intercept form, or for horizontal and vertical lines. Examples are provided for finding slopes and writing equations in different forms.
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This document discusses how to graph linear equations on a coordinate plane using different methods:
1) Using two points from the linear equation to plot and connect those points
2) Using the x-intercept and y-intercept, which are the points where the line crosses the x- and y-axes
3) Using the slope of the line and the y-intercept, where the slope is rise over run and the y-intercept is where the line crosses the y-axis
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This document provides an overview of slope and how it is calculated and represented in algebra. It defines slope as rise over run and shows how to calculate it by counting squares between two points on a graph. Positive and negative slopes are introduced, as well as the slope-intercept form of a line, y=mx+b, where m is the slope and b is the y-intercept. Examples are given of calculating slope from points and graphing lines in slope-intercept form. Requirements for using the point-slope form, y-y1=m(x-x1), are also outlined.
Slope of a line study guide
The slope of a line represents its steepness and is calculated as the ratio of rise over run, or the vertical change over the horizontal change between two points on the line. To find the slope, identify two points, count the vertical and horizontal change between them, and divide the vertical change by the horizontal change. A positive slope occurs when the vertical change is up or the horizontal change is left to right, while a negative slope occurs when the vertical change is down or the horizontal change is right to left.
Slope of a Line SIM.docx
1) The document discusses finding the slope of a line passing through two points. It provides the definition of slope as the ratio of the rise over the run between two points on a line.
2) It gives the algebraic formula for calculating the slope as m = (y2 - y1) / (x2 - x1), where m is the slope and the subscripts 1 and 2 refer to the x- and y-coordinates of the two points.
3) Several examples are shown of calculating the numeric value of the slope given two points on a line.
Finding slope
This is a ppt for learning how to calculate the slope of a line within a line graph. This ppt works for about a 8th t 9th grade level.
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Parallel And Perpendicular Nov 24
1) Parallel lines have the same slope, while perpendicular lines have slopes that are negative reciprocals of each other.
2) The document provides examples of finding slopes of parallel and perpendicular lines, including writing equations of lines given certain points and conditions.
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The document defines slope as the steepness and direction of a line, calculated as the rise over the run or change in y over the change in x between two points on the line. It provides examples of calculating the slope between two points and finding the y-value of a third point given the slope. It also describes how the sign of the slope indicates whether a line is diagonal up/right, horizontal, or diagonal down/right and when the slope is undefined when the line is vertical.
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Nov 17 Slope
- 1. 1
- 2. Slope of a Line refers to the steepness and direction of a line rise change in y (vertical) Slope = run = change in x (horizontal) Ramp A Ramp B 6m 3m 12m 12m 2
- 3. rise change in y (vertical) Slope = run = change in x (horizontal) m = y2 y1 Example: x2 x1 Find the slope of the line that passes through (3, 2) and (5,1 ) 3
- 6. 6
- 7. 7
- 8. • if m > 0, line is diagonal and ____ to the right • if m = 0, line is ____________ • if m < 0, line is diagonal and _____ to the right • if m is undefined (denominator = 0), line is ___________ 8
- 9. Assignment Exercise # 7 9