1) The document provides examples of finding the slope and y-intercept of linear equations and using intercepts to graph lines. It also includes word problems that can be represented by systems of linear equations. 2) Interpreting intercepts is discussed. The x-intercept represents the point where the line crosses the x-axis, and the y-intercept is where it crosses the y-axis. 3) Graphs are helpful for interpreting real-world situations represented by linear equations and systems of equations. The intercepts can show the breakpoint values where variables are equal to zero.

1. Course 3, Lesson 3-5
State the slope and the y-intercept for the graph of each equation.
1. y = 2x + 1 2. y = 3x + 2
3. y = –2x + 4.5 4. 3x – y = 4
5. The total price of apples y at an orchard can be calculated with the
equation 1.12x + 5 = y, where x is the number of pounds of apples
picked. What does the slope represent?
6. What is the equation of the graph
at the right?

2. Course 3, Lesson 3-5
ANSWERS
1. m = 2; b = 1
2. m = 3; b = 2
3. m = -2; b = 4.5
4. m = 3; b = -4
5. the price of apples per pound
6.
1
2
2
 y x

3. WHY are graphs helpful?
Expressions and Equations
Course 3, Lesson 3-5

4. • Preparation for 8.EE.8c
Solve real-world and mathematical problems leading to two linear equations in
two variables.
Mathematical Practices
1 Make sense of problems and persevere in solving them.
3 Construct viable arguments and critique the reasoning of others.
4 Model with mathematics.
Course 3, Lesson 3-5 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council
of Chief State School Officers. All rights reserved.
Expressions and Equations

5. To find the x- and y- intercept
• using the slope intercept form of a
linear equation
• using the standard form of a linear
equation
Course 3, Lesson 3-5
Expressions and Equations

6. • x-intercept
• standard form
Course 3, Lesson 3-5
Expressions and Equations

7. 1
Need Another Example?
2
3
Step-by-Step Example
1. State the x- and y-intercepts of y = 1.5x – 9. Then use the
intercepts to graph the equation.
First find the y-intercept.
y = 1.5x + (–9)
b = –9
Write the equation in the form y = mx + b.
To find the x-intercept, let y = 0.
0 = 1.5x – 9
Graph the points (6, 0)
and (0, –9) on a coordinate
plane.
Write the equation. Let y = 0.
9 = 1.5x Addition Property of Equality
Division Property of Equality
6 = x Simplify.
Then connect the points.

8. Answer
Need Another Example?
State the x- and y-intercept of the function y = x – 2.
Then graph the function.
x-intercept: 3;
y-intercept = –2

9. 1
Need Another Example?
2
3
Step-by-Step Example
2. Mauldin Middle School wants to make $4,740 from yearbooks.
Print yearbooks x cost $60 and digital yearbooks y cost $15.
This can be represented by the equation 60x + 15y = 4,740.
To find the x-intercept, let y = 0. To find the y-intercept, let x = 0.
60x + 15y = 4,740
60x + 15(0) = 4,740
60x = 4,740
x = 79
Use the x- and y-intercepts to graph the equation.
60x + 15y = 4,740
60(0) + 15y = 4,740
15y = 4,740
y = 316

10. Answer
Need Another Example?
The drama department sold $1,260 worth of tickets to a
play. Student tickets x cost $5 and adult tickets y cost $9.
This can be represented by the equation 5x + 9y = 1,260.
Use the x- and y-intercepts to graph the equation.
The x-intercept of 252 means that if 252 student
tickets and 0 adult tickets were sold, the total
sales would be $1,260. The y-intercept of 140
means that if 0 student tickets and 140 adult
tickets were
sold, the total
sales would
be $1,260.

11. 1
Need Another Example?
2
Step-by-Step Example
3. Mauldin Middle School wants to make $4,740 from yearbooks.
Print yearbooks x cost $60 and digital yearbooks y cost $15.
This can be represented by the equation 60x + 15y = 4,740.
The x-intercept is at the point (79, 0). This
means they can sell 79 print yearbooks and
0 digital yearbooks to earn $4,740.
Interpret the x- and y-intercepts.
The y-intercept is at the point (0, 316). This
means they can sell 0 print yearbooks and
316 digital yearbooks to earn $4,740.

12. Answer
Need Another Example?
The drama department sold $1,260 worth of tickets
to a play. Student tickets x cost $5 and adult tickets
y cost $9. This can be represented by the equation
5x + 9y = 1,260. Interpret the intercepts.
The x-intercept of 252 means that if 252 student
tickets and 0 adult tickets were sold, the total sales
would be $1,260. The y-intercept of 140 means
that if 0 student tickets and 140 adult tickets were
sold, the total sales would be $1,260.

13. How did what you learned
today help you answer the
WHY are graphs helpful?
Course 3, Lesson 3-5
Expressions and Equations

14. How did what you learned
today help you answer the
WHY are graphs helpful?
Course 3, Lesson 3-5
Expressions and Equations
Sample answer:
• In a real-world situation, a graph can help you interpret
the x- and y-intercepts.

15. Find the x- and y-intercepts
of the equation −x + 3y = 12
and use the intercepts to
graph the function.
Ratios and Proportional RelationshipsExpressions and Equations
Course 3, Lesson 3-5