Skill: Determine rate of change from an equation

To find the rate of change, write the equation in the form

$$y=mx+b$$

The coefficient $m$ of $x$ is the rate of change. It tells how much $y$ changes when $x$ increases by 1. The number $b$ is the starting value, not the rate of change.

Example: Find the rate of change in

$$y=-\frac{1}{2}x+6$$

Step 1: Identify the coefficient of $x$.

The coefficient of $x$ is

$$-\frac{1}{2}$$

So, the rate of change is

$$\boxed{-\frac{1}{2}}$$

Step 2: Interpret the rate.

For every increase of 1 in $x$, the value of $y$ decreases by $\frac{1}{2}$.

The negative sign means the relationship is decreasing. The $6$ is the initial value, or $y$-intercept, not the rate of change.