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Linear Functions
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Basic Concepts on Linear Functions

Example 2

Express each equation in the form y=mx+b.

a. 2x+7y=−3
b. 1 3 x+y=−1
c. 5x−y=2


Solution

a. Apply the properties of equality.

2x+7y = −3 Given
2x+7y−2x = −3−2x Subtract 2x from both sides.
7y = −3−2x Simplify.
y = − 3 7 − 2 7 x Multiply both sides by 1 7 .
y = − 2 7 x− 3 7 Rearrange the terms.

Thus, the equation becomes y=− 2 7 x− 3 7 , where m=− 2 7 and b=− 3 7 .

b. Apply the subtraction property of equality.

1 3 x+y = −1 Given
1 3 x+y− 1 3 x = −1− 1 3 x Subtract 1 3 x from both sides.
y = −1− 1 3 x Simplify.
y = − 1 3 x−1 Rearrange the terms.

Thus, the equation becomes y=− 1 3 x−1, where m=− 1 3 and b=−1.

c. Apply the properties of equality.

5x−y = 2 Given
5x−y−5x = 2−5x Subtract 5x from both sides.
−y = 2−5x Simplify.
y = 5x−2 Rearrange the terms.

Thus, the equation becomes y=5x−2, where m=5 and b=−2.