Notes on 3.2 properties of linear frunction graphs
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The document discusses key properties of linear function graphs, including that the y-intercept is the y-value when x=0 and the x-intercept is the x-value when y=0. It defines slope as m in the slope-intercept equation y=mx+b and describes horizontal and vertical lines having slopes of 0 and undefined respectively. It lists three common forms for linear functions: slope-intercept, point-slope, and Ax+By=C and provides examples of transforming between the forms.
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4. The remainder of the class will cover topics on quadratic functions including graphing quadratic functions in standard, vertex, and intercept forms as well as solving quadratic equations through factoring and using the quadratic formula.
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
identities1.2
The document discusses the concept of slope and how it is used to describe the steepness of a line. It defines slope as the ratio of the vertical change (rise) to the horizontal change (run) between two points on a line. Several forms of linear equations are presented, including point-slope form, slope-intercept form, and standard form. Relationships between parallel and perpendicular lines based on their slopes are also described. Examples are provided to demonstrate finding slopes, writing equations of lines, and determining if lines are parallel or perpendicular based on their slopes.
Mathematics 8 Linear Functions
This document provides a module on linear functions. It defines linear functions as those that can be written in the form f(x) = mx + b, where m is the slope and b is the y-intercept. The module teaches how to determine if a function is linear, rewrite linear equations in slope-intercept form, and graph linear functions given various inputs like two points, x- and y-intercepts, slope and a point, or slope and y-intercept. Examples and practice problems are provided to help students learn to identify, write, and graph different types of linear functions.
Module 1 linear functions
This module introduces linear functions. It defines a linear function as one that can be written in the form f(x) = mx + b, where m is the slope and b is the y-intercept. It explains how to graph linear functions given two points, the x- and y-intercepts, the slope and a point, or the slope and y-intercept. The document provides examples and practice problems for students to learn how to represent linear functions in different forms, rewrite them between standard and slope-intercept form, and graph them based on given information.
Functions
1. The document discusses functions and their graphical representations. It defines key terms like domain, range, independent and dependent variables.
2. It provides examples of different types of functions including constant, linear, quadratic, and rational functions. Linear functions have a straight line graph, quadratic functions have a parabolic graph, and rational functions have a hyperbolic graph.
3. The document also discusses how to graph systems of equations, which can have a single solution point (consistent independent), infinite solutions along the same line (consistent dependent), or no solution (inconsistent parallel lines).
PPT (01-13-21).pptx
This document discusses various methods for graphing linear functions:
1. Any function of the form f(x) = mx + b, where m is not 0, is a linear function. The graph of a linear function is a straight line with slope m and y-intercept b.
2. Linear functions can be graphed using a table of values by plotting the points and connecting them with a straight line.
3. The intercept method graphs a linear function by finding the x-intercept where the line crosses the x-axis and the y-intercept where it crosses the y-axis and connecting those two points.
6.6 analyzing graphs of quadratic functions
This document discusses analyzing and graphing quadratic functions. It defines key terms like vertex, axis of symmetry, and vertex form. It explains that the graph of y=ax^2 is a parabola, and how the value of a affects whether the parabola opens up or down. It also describes how to graph quadratic functions in vertex form by plotting the vertex and axis of symmetry, and using symmetry.
April 10, 2015
The document discusses graphing quadratic functions. It begins with reviewing key concepts like the vertex and axis of symmetry. The effects of the a, b, and c coefficients on the parabola are explained. Examples are provided to show how changing these values affects the width, direction opened, and vertical translation of the graph. The class will graph various quadratic functions by finding the axis of symmetry, vertex, y-intercept, and other points to plot the parabola. Students are assigned class work problems to graph quadratic functions and show their work.
Line and its slope
1. The document discusses various forms of linear equations including standard form (Ax + By = C), slope-intercept form (y = mx + b), and point-slope form (y - y1 = m(x - x1)).
2. It provides examples of transforming linear functions between these forms and discusses how to find the slope and y-intercept of a linear function from its graph.
3. The slope and direction of a linear function's graph is determined by whether its slope is positive or negative. A positive slope produces an upward rising line while a negative slope produces a downward falling line.
January 9, 2014
The document provides information about linear equations and graphs:
- It defines the slope formula for finding the slope between two points on a line.
- It explains the slope-intercept form of a linear equation where y=mx+b, with m being the slope and b being the y-intercept.
- It gives examples of writing equations in slope-intercept form and graphing lines from their equations.
- It discusses other forms like point-slope form and how to write equations of lines given characteristics like a point and slope.
- It defines parallel and perpendicular lines based on their slopes being equal or negative reciprocals, respectively.
@ Business Mathematics Chapter 1& 2.pptx
This document provides an overview of the course "Business Mathematics" which covers topics like linear equations, nonlinear equations, and economic applications of linear and quadratic models. The course is targeted at second year ABVM students.
Unit one discusses linear equations, their basic concepts and properties. It also covers developing linear equations using the slope-intercept form, slope-point form, and two-point form. Nonlinear equations are defined as equations with terms of degree two or higher that do not represent straight lines.
Economic applications of linear and quadratic models are also discussed. Functions and curves are defined in economics, with examples like the relationship between money earned and hours worked given as a simple linear function.
April 9, 2015
The document discusses graphing quadratic functions. It begins with reviewing key concepts like the vertex and axis of symmetry and how the a, b, and c coefficients affect the graph. Examples are provided for determining the width, direction opened, and vertical shift based on these coefficients. The remainder of the document provides step-by-step examples of graphing quadratic functions by finding the axis of symmetry, vertex, y-intercept, and other points to plot the parabolic curve.
2.4 Linear Functions
This document defines and discusses linear functions. It covers calculating the slope between two points, graphing linear functions in slope-intercept form, and finding the slope from an equation. Key points include: linear functions have a constant rate of change; the slope is defined as rise over run; and a linear function can be written in standard, point-slope, or slope-intercept form. Examples are provided for graphing a linear function from its slope-intercept equation and finding the slope between two points or from a linear equation.
2.5 Equations of Lines
This document discusses equations of lines, including linear functions and their standard, point-slope, and slope-intercept forms. It defines parallel and perpendicular lines based on their slopes. It provides examples of writing the equation of a line from its graph or from a point and slope. Key steps include calculating the slope, selecting a point, and writing the equation in the appropriate form.
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Here are the steps to solve this problem:
Let x = one number
Let y = the other number
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Notes on 3.2 properties of linear frunction graphs
- 5. “ Ax + By = C” Form