Question

6.Which of the following represents a graph with a rate of change of ?

Answer 1

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,

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

Considering two clear points from graph C, picking the points (2,-1) and (4,0)

`\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=(y_2-y_1)/(x_2-x_1) \\ m=(0-(-1))/(4-2) \\ m=(0+1)/(4-2) \\ m=(1)/(2) \end{gathered}`

Therefore, the graph that represents a rate of change of 1/2 is the graph of option C.