From the graph we identify 4 points
[tex]\begin{gathered} (0,7)\to P1 \\ (1,7.5)\to P2 \\ \mleft(2,8\mright)_{}\to P3 \\ (3,8.5)\to P4 \end{gathered}[/tex]
To find the ratio we use the following equation
[tex]m=\frac{y_2-y_1}{x_2-x_1}_{}[/tex]
We plug in the values of the chosen points (P1 and P2) to find the slope:
[tex]\begin{gathered} m_{1,2}=\frac{7.5-7}{1-0} \\ m_{1,2}=\frac{0.5}{1} \\ m_{1,2}=0.5 \end{gathered}[/tex]
Now, we find the slope for another pair of points (P3 and P4)
[tex]\begin{gathered} m_{3,4}=\frac{8.5-8}{3-2} \\ m_{3,4}=\frac{0.5}{1} \\ m_{3,4}=0.5 \end{gathered}[/tex]
We can observe that the rate of change is constant for all points obtaining a slope of 0.5
