Question

1. a table of values for a linear function is shown. what is the rate of change for this function?

x | 1 | 2 | 3 | 4
y | 7 | 9 | 11 | 13

Explanation:

Step1: Recall rate of change formula

The rate of change (slope) for a linear function is $\frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}$

Step2: Pick two table points

Use $(x_1,y_1)=(1,7)$ and $(x_2,y_2)=(2,9)$

Step3: Calculate the rate of change

$\frac{9 - 7}{2 - 1} = \frac{2}{1} = 2$
(Verify with other pairs: $\frac{11-9}{3-2}=2$, $\frac{13-11}{4-3}=2$)

Answer:

2