A

1
5-Minute Check 1
Which equation best describes the sequence 9,
10, 11, 12, ?
Find the 22nd term of the sequence 7, 10, 13, 16,
.

1. A
2. B
3. C
4. D

Jimmy increased his trumpet practice by 10
minutes each week. He practiced 15 minutes during
Week 1. How many minutes did he practice during
Week 12?
2
Splash Screen
3
Then/Now
You used functions to describe relationships
between two quantities. (Lesson 15)

• Solve linear equations with two variables.

• Graph linear equations using ordered pairs.

4
Vocabulary

• linear equation

An equation in which the variables appear in
separate terms and neither variable contains an
exponent other than 1. The graph of a linear
equation is a straight line.

• x-intercept
• y-intercept

The x-coordinate of a point where a graph crosses
the x-axis (x, 0)
The y-coordinate of a point where a graph crosses
the y-axis (0, y)
5
Example 1
Use a Table of Ordered Pairs
Find four solutions of y 4x 3. Write the
solutions as ordered pairs.
Choose four values for x. Then substitute each
value into the equation to solve for y. There are
many possible solutions. The solutions you find
depend on which x-values you choose.
6
Example 1
Use a Table of Ordered Pairs
Sample Answer Four possible solutions are (0,
3), (1, 7), (2, 11), and (3, 15).
7
Example 1
Find four solutions of y 2x 4.
A. (1, 2), (3, 2), (5, 1), and (7, 10) B. (2,
0), (0, 4), (2, 0), and (4, 4) C. (0, 4), (1,
2), (2, 2), and (3, 1) D. (0, 4), (1, 2),
(2, 0), and (3, 2)

1. A
2. B
3. C
4. D

8
Example 2
Use Function Equations
BUSINESS At a local software company, Level 1
employees x earn 48,000 and Level 2 employees y
earn 24,000. Find four solutions of 48,000x
24,000y 216,000 to determine how many employees
at each level the company can hire for 216,000.
Explain each solution.
First, rewrite the equation by solving for y.
9
Example 2
Use Function Equations
48,000x 24,000y 216,000 Write the
equation. 24,000y 216,000
48,000x Subtract 48,000x from each side.
Divide each side by 24,000.
y 9 2x Simplify.
10
Example 2
Use Function Equations
Choose four x-values and substitute them into y
9 2x.
Sample Answer (0, 9), (1, 7), (2, 5), and (3,
3) 0 employees at Level 1, 9 employees at Level
2 1 employee at Level 1, 7 employees at Level 2 2
employees at Level 1, 5 employees at Level 2 3
employees at Level 1, 3 employees at Level 2
11
Example 2
BOOKS At a local bookstore, hardbacks are on
sale for 6 and paperbacks are on sale for 3.
Bob has 42 to spend on books. Find four
solutions to determine how many books of each
type Bob can buy with his 42.
A. 0 hardbacks, 42 paperbacks3 hardbacks, 24
paperbacks5 hardbacks, 12 paperbacks7
hardbacks, 0 paperbacks B. 0 hardbacks, 14
paperbacks1 hardbacks, 12 paperbacks2
hardbacks, 10 paperbacks3 hardbacks, 8
paperbacks C. 0 hardbacks, 42 paperbacks3
hardbacks, 24 paperbacks5 hardbacks, 9
paperbacks7 hardbacks, 7 paperbacks D. 0
hardbacks, 14 paperbacks1 hardbacks, 8
paperbacks2 hardbacks, 2 paperbacks3 hardbacks,
4 paperbacks

1. A
2. B
3. C
4. D

12
Example 3
Graph a Linear Function
Graph y x 2.
Step 1 Find the x-intercept. To find the
x-intercept, let y 0.
y x 2 Write the equation. 0 x 2 Replace
y with 0. 2 x Subtract 2 from each side.
Since x 2 when y 0, graph the ordered pair
(2, 0).
13
Example 3
Graph a Linear Function
Step 2 Find the y-intercept.
y x 2 Write the equation. y 0 2 Replace
x with 0. y 2 Simplify.
Since y 2 when x 0, graph the ordered pair
(0, 2).
Step 3 Connect the points with a line.
14
Example 3
Graph a Linear Function
Check Check another point in the equation. If x
1, y 1 2 or 3. Notice that (1, 3) is
on the graph of the line.
15
Example 3
Graph y 5 x.

1. A
2. B
3. C
4. D

16
End of the Lesson