Solution:
The rate of change of a graph is the same as the slope of the graph.
The graph that has a rate of change of 1/2 is the graph with a slope of 1/2.
To calculate the slope of a graph,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Considering two clear points from graph C, picking the points (2,-1) and (4,0)
[tex]\begin{gathered} \text{where} \\ x_1=2 \\ y_1=-1 \\ x_2=4 \\ y_2=0 \\ \\ \text{Substituting these values in the formula to get slope,} \\ m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{0-(-1)}{4-2} \\ m=\frac{0+1}{4-2} \\ m=\frac{1}{2} \end{gathered}[/tex]Therefore, the graph that represents a rate of change of 1/2 is the graph of option C.