Question

How can i find the rate of change in the graph of the photo?

Answer 1

The rate of change in a linear graph is the slope m of the line. The slope equation is given by

$m=\frac{y_2-y_1}{x_2-x_1}$

where the x's and y's coming from two points in the given graph. For instance, we can choose from the given line:

$\begin{gathered} (x_1,y_1)=(-2,0) \\ (x_2,y_2)=(0,4) \end{gathered}$

By substituying these values into the slope formula, we obtain

$m=\frac{4-0}{0-(-2)}$

which gives

$\begin{gathered} m=\frac{4}{2} \\ m=2 \end{gathered}$

hence, the rate of change is 2.