Page 86 - Math Course 3 (Book 1)

Linear Equations

Solve an Equation for y Four solutions are (–1, –4), (0, –3), (1, –2),
and (2, –1).
Example
Plot these ordered pairs and draw a line through
them. Note that the ordered pair for any point on
BUSINESS this line is a solution of y = x – 3. The line is a
At a local software company, Level 1 employees complete graph of the function.
x earn $48,000 and Level 2 employees y earn
$24,000. Find four solutions of 48,000x + 24,000y Answer
= 216,000 to determine how many employees at
each level the company can hire for $216,000.

First, rewrite the equation by solving for y. y = x – 3

48,000x + 24,000y = 216,000 Write the equation.

24,000y = 216,000 – 48,000x Subtract 48,000x (2, –1)
from each side.
(1, –2)
24,000y = 216,000 48,000x Divide each side by (–1, –4) (0, –3)
–
24,000 24,000 24,000 24,000.
y = 9 – 2x Simplify.
Check
Choose four x values and substitute them into It appears from the graph that (4, 1) is also a
y = 9 – 2x. solution. Check this by substitution.

y = x – 3 Write the equation.
x y = 9–2x y (x, y)
1 = 4 – 3 Replace x with 4 and y
0 y = 9–2(0) 9 (0, 0) with 1.
1 y = 9–2(1) 7 (1, 1)
1 = 1 Simplify.
2 y = 9–2(2) 5 (2, 5)
3 y = 9–2(3) 3 (3, 3)
Your Turn!

(0, 9), (1, 7), (2, 5), and (3, 3)
0 Level 1, 9 Level 2 Use a Table of Ordered Pairs
Answer 1 Level 1, 7 Level 2
2 Level 1, 5 Level 2 Find four solutions of y = 2x – 4.
3 Level 1, 3 Level 2
A. (1, –2), (3, 2), (5, 1), and (7, 10)
B. (–2, 0), (0, –4), (2, 0), and (4, 4)
Graph a Linear Equation C. (0, –4), (1, –2), (2, 2), and (3, –1)
D. (0, –4), (1, –2), (2, 0), and (3, 2)
Example
Answer

Graph y = x – 3 by plotting ordered pairs.
First, find ordered pair solutions.

x y = x – 3 y (x, y)
–1 y = (–1) – 3 –4 (–1, –4)

0 y = (0) – 3 –3 (0, –3)

1 y = (1) – 3 –2 (1, –2)
2 y = (2) – 3 –1 (2, –1)

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