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Graphing and Writing Linear Functions
SOLVING EQUATIONS INVOLVING RATIONAL EXPONENTS
Linear Equations and Graphing
Systems of Linear Equations
Solving Polynomial Equations
Matrix Equations and Solving Systems of Linear Equations
Introduction Part II and Solving Equations
Linear Algebra
Graphing Linear Inequalities
Using Augmented Matrices to Solve Systems of Linear Equations
Solving Linear Inequalities
Solution of the Equations
Linear Equations
Annotated Bibliography of Linear Algebra Books
Write Linear Equations in Standard Form
Graphing Linear Inequalities
Introduction to Linear Algebra for Engineers
Solving Quadratic Equations
THE HISTORY OF SOLVING QUADRATIC EQUATIONS
Systems of Linear Equations
Review for First Order Differential Equations
Systems of Nonlinear Equations & their solutions
LINEAR LEAST SQUARES FIT MAPPING METHOD FOR INFORMATION RETRIEVAL FROM NATURAL LANGUAGE TEXTS
Quadratic Equations
Syllabus for Differential Equations and Linear Alg
Linear Equations and Matrices
Solving Linear Equations
Slope-intercept form of the equation
Linear Equations
DETAILED SOLUTIONS AND CONCEPTS QUADRATIC EQUATIONS
Linear Equation Problems
Systems of Differential Equations
Linear Algebra Syllabus
Quadratic Equations and Problem Solving
LinearEquations
The Slope-Intercept Form of the Equation
Final Exam for Matrices and Linear Equations
Linear Equations
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Slope-intercept form of the equation

Key Concepts: Slope-intercept form of the equation of a line
Martin-Gaye sections and practice problems
3.5: 1 – 51 odd, 53 – 58 all

Example 1
The line 3 x + 2 y = 2 is shown in Figure 1.

a. Find two points on the line and verify that they in fact satisfy the equation 3 x + 2 y = 2 .

b. Find the slope and y-intercept of the line.

c. Solve the equation 3 x + 2 y = 2 for y . State the connection between this new equation and
the slope and y-intercept of the line.

Example 2
The line 4 x − 3 y = 6 is shown in Figure 2.
a. Find two points on the line and verify that they in fact satisfy the equation 4 x − 3 y = 6.
b. Find the slope and y-intercept of the line.
c. Solve the equation 4 x − 3 y = 6 for y . State the connection between this new equation and
the slope and y-intercept of the line.



Definition and most awesome fact
The equation y = m x + b is called the slope-intercept form of a linear equation.
The equation of any non-vertical line can be written in this form. When the equation is written in this
form, the number m is the slope of the line and the point (0,b) is the y-intercept of the line.

Example 3
State the slope and y-intercept of the line with equation
. Graph the line onto Figure 3.

Example 4
State the slope and y-intercept of the line with equation
y = − 4. Graph the line onto Figure 4.

Example 5
State the slope and y-intercept of the line with equation
−3 x − 5 y = 4 . Graph the line onto Figure 5.

Example 6
State the slope and y-intercept of the line with
equation x = − 5. Graph the line onto Figure 6.

Example 7
a. Find an equation for the line in Figure 7.
b. Find an equation for the line parallel to the given line
that passes through the point (6,5).

Example 8
Find an equation for the line shown in Figure 8.

 

Example 9
Find an equation for the line that passes through the points (−2,3) and (−7,1) .

 

Example 10
Find an equation for the line that is parallel to the line with equation 6 y = x + 2 and passes
through the point (12, 2) .

 

Example 11
Find an equation for the line that is perpendicular to the
line in Figure 9 and passes through the point (1,1) .