Question

If a linear function has the points (9,−5) and (−2,−2) on its graph, what is the rate of change of the function?

Answer 1

The linear function has the points (9,-5) and (-2,-2) on its graph.

The rate of change is the slope of the line.

It is given by:

`m=(y_2-y_1)/(x_2-x_1)`

Substitute the values:

`(x_1,y_1)=(9,-5);(x_2,y_2)=(-2,-2)`

The rate of change m is given by:

`\begin{gathered} m=(-2-(-5))/(-2-9) \\ m=(-2+5)/(-11) \\ m=-(3)/(11) \end{gathered}`

Hence the rate of change is -3/11 or -0.27.