Question

5.Mrs. Marley invested $1500 in a savings account. The graph below shows the value ofthe investment over a period of time. Which of the following situations best describesthe rate of change?Value (dollars)2.500A. The value of the investment increases by $200each year.B. The value of the investment increases by $1002000each year.C. The value of the investment decreases by $100each year.D. The value of the investment decreases by $200each year.Time (years)

Answer 1

In order to solve this question, we need to find the slope of the given line. From the graph, we can choose two points, for instance,

`\begin{gathered} (x_1,y_1)=(0,1500) \\ (x_2,y_2)=(10,2500) \end{gathered}`

then, the slope is given by

`\begin{gathered} m=(y_2-y_1)/(x_2-x_1) \\ m=(2500-1500)/(10-0) \\ \text{then} \\ m=(1000)/(10) \\ m=100 \end{gathered}`

since m is positive, then the value of the investment increases by $100 each year, which corrpesponds to option B