Evaluate each expression when x = −2.

1. 4x + 10

2. −3 + 11x

3.

4. 8(x + 5)

x21

Warm-Up 10.1.15

2

−25

−1

24

Good to Know!The Commutative Property of Addition states that numbers can be added in any order. This can be applied in a linear equation.

In Lesson 2.5, linear equations were shown in the form:

y = b ± mx

Based on the Commutative Property, this equation can also be written as:

y = mx ± b

For example, y = 7 + 2x y = 2x + 7y = 4 – 3x y = –3x + 4

Notice that the “ – ” belongs to the rate of change and

must move with it.

Explore! Linear Qualities

Use the linear equations given in the box to complete this activity.

Step 1 List the equation(s) that have a negative rate of change.

Step 2 List the equations(s) that have a positive y-intercept.

Step 3 Which equation has a start value of zero? How do you know?

Explore! Multi-Step Equation

Step 4 Which equation has a rate of change equal to zero? How do you know?

Step 5 Create your own linear equation that fits the given description.

a. A positive start value and negativerate of change.

b. A rate of change equal to zero.

c. A start value equal to zero.

d. A negative rate of change and a negative y-intercept.

Use the linear equation to complete the input-output table:

y = 3x + 8

Substitute each x-value intothe equation to determine the y-values.

Example 1

Good to Know!Any input-output table can be turned into ordered pairs and graphed. When dealing with linear equations, graphing is a great way to double-check the calculations as all points should be in a straight line.

The graph below shows the ordered pairs from the table used in Example 3.

Complete the following table for the linear equation y = −2x + 1.

x y−3029

Exit Problem

−17−3

1

7