Question

this graph ( below ) shows how thr total number of pieces greta knows how to sing depends on the number of weeks she takes voice lessons . what is the rate of change .

Answer 1

The rate of change of the line is equal to its slope. To calculate the slope, choose two points on the line and write down their coordinates.

Take the points:

`\begin{gathered} (0,4) \\ (5,6) \end{gathered}`

Given two arbitrary points:

`\begin{gathered} (x_1,y_1) \\ (x_2,y_2) \end{gathered}`

The slope between them is given by the equation:

`m=\frac{y_2-y_1}{x_2-x_1_{}}`

Substitute y_2=6, y_1=4, x_2=5 and x_1=0 into the formula for the slope to find the rate of change:

`\begin{gathered} m=(6-4)/(5-0) \\ =(2)/(5) \end{gathered}`

Therefore, the rate of change of the vocal pieces that Greta can sing over the weeks that she takes voice lessons, is 2/5.