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:
[tex]\begin{gathered} (0,4) \\ (5,6) \end{gathered}[/tex]
Given two arbitrary points:
[tex]\begin{gathered} (x_1,y_1) \\ (x_2,y_2) \end{gathered}[/tex]
The slope between them is given by the equation:
[tex]m=\frac{y_2-y_1}{x_2-x_1_{}}[/tex]
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:
[tex]\begin{gathered} m=\frac{6-4}{5-0} \\ =\frac{2}{5} \end{gathered}[/tex]
Therefore, the rate of change of the vocal pieces that Greta can sing over the weeks that she takes voice lessons, is 2/5.
