Answer Key
Equations of Linear Relations
-
University:
University of Central Arkansas -
Course:
MATH 1486 | Calculus Preparation Academic year:
2024
-
Views:
247
Pages:
62
Author:
Haleigh Chase
Equations of Linear Relations Lesson #1: The Equation of a Line in
Slope y-intercept Form → y = mx + b
Overview of Unit
In this unit we express the equation of a linear relation in three different forms: slope y-intercept form, point-slope form, and general form. We relate linear relations expressed in these forms to their graphs.
We also determine the linear relation given: a graph, a table of data points, a point and the slope, two points, a point and the equation of a parallel or perpendicular line.
Investigating the Graphs of Linear and Non-Linear Relations
a) The equations of the graphs of some relations are given. In each case, use a graphing calculator to sketch the graph of the relation and make a rough sketch of the graph on the grid provided. Do not list any z- or y-intercepts.
y=3x+1
y=-2x+3
y=-x+1
y=x2-3
***
1 y=x-2
y=4x
y=2
+++
b) List the equations of the graphs as linear or non-linear.
LINEAR: y=3x+1 yo-airs, yo-z, y.x
NON-LINEAR:
c) Compare the lists. Write a rule from the equation which can be used to determine whether the graph is a straight line or not.
If the exponents of the term in x and the term in y to one, then the graph is a straight line. are both equal
Copyright © by Absolute Value Publications. This book is NOT covered by the Cancopy agreement.
390 Equations of Linear Relations Lesson #1. The Equation of a Line in Slope y-intercept Form.....
Linear Equation
A linear equation is an equation of the form y=mx+b, where m, be R. The graph of a linear equation is a straight line.
Investigating m and b in the equation y=mx+b
Part One
3
2 y=x-1
Jenine used a graphing calculator to sketch the graph 2 of the linear equation y=x-1 Her sketch is shown on the grid.
3B
a) Use the sketch and points A and B to find the 2 slope and y-intercept of the graph of y=x-1. Sloperise run
Yint -13
(+)
A
3
b) Compare the values found in a) with the coefficient of x and the constant term in the equation y=3x-1.
The slope is the coefficient of x. (SAME) The y-intercept is the coostant term. (SAME)
c) Jenine sketched the graphs of two more linear equations. Use the grid to determine the slope and y-intercept of each graph.
equation
slope
4
y-intercept
3
y=2x+1
y=2x+1 57
-5
2
2
d) Make a conjecture about the slope and y-intercept of the graph of the linear equation y = mx + b. Slope = m y-int = b
(4)
y=-x-3
Copyright by Absolute Value Publications. This book is NOT covered by the Cancopy agreement.
Equations of Linear Relations Lesson #2: Writing Equations Using y = mx + b
Review
We have learned that the graph of an equation in the form y=mx+b is a straight line with slope m and y-intercept b.
Using the Form y=mx+b to Write the Equation of a Line
The form y=mx+b can be used to determine the equation of a line when the following information is given:
the slope of the line the y-intercept of the line.
Yint
Class Ex.
Write the equation of a line passing through the point( (0,2) with slope
5
mo slope = b. Ynk 2
y=x+2
Clour Ex. 42
Each line on the grid passes through points with integer coordinates. In each case, state the slope and y-intercept of the line, and determine the equation of the line.
2
5
line 1(2):
line 2(2):
no Slope =
mo sloje
bfint-4
bogist 2
y3x+2
Class Ex. 13
Determine the equation of the following lines.
1 a) The line parallel to y=x+4, and with the same y-intercept as y = 6x-7.
3
w
equation gox-7
b) The line passing through (0,9), and perpendicular to the line joining (2,-6) and (-5,0).
-5-2
perpendicular slope. I
Copyright © by Absolute Value Publications. This book is NOT covered by the Cancopy agreement.
Jint 9
equation y=7x+9
Related Documents
- 2.1 Exponents Laws - Notes [Teacher]
- A Guide to Understanding Variables and Equations
- Trigonometric Limit Theorem: Applications in Calculations
- 1.4 Quadratics - Max or Min - Worksheet 1 [Answers]
- 1.3 Radicals - Worksheet 1 [Answers]
- 1.4 Quadratics - Max or Min - Notes [Teacher]
- 1.6 Quadratics - Roots - Notes [Teacher]
- 1.6 Quadratics - Roots - Worksheet 1 [Answers]
- 1.7 Quadratics - Linear Systems - Notes [Teacher]
- 1.7 Quadratics - Linear Systems - Worksheet 1 [Answers]
- 1.1 Functions, Domain, & Range - Notes [Teacher]
- Maximum and Minimum in Function Graphs: Determination and Understanding
- Graph Analysis: Functions, Domain, Range
- Mapping Functions of Two Variables Using Maple 13
- Matrix Multiplication in Linear Algebra
- 1.3 Radicals - Notes [Teacher]
- 1.0 Factoring - Notes
- 1.0 Factoring - Worksheet 1 [Questions + Answers]
- An Detailed Guide to Understanding Real Numbers
- 1.2 Function Notation - Textbook [Questions + Answers]
Equations of Linear Relations
of 62
Recommended Documents
Report
Tell us what’s wrong with it:
Thanks, got it!
We will moderate it soon!
Free up your schedule!
Our EduBirdie Experts Are Here for You 24/7! Just fill out a form and let us know how we can assist you.
Take 5 seconds to unlock
Enter your email below and get instant access to your document