Question

the graph below shows the distance in miles, ( d ), biked from a camp at ( t ) hours.

what hourly interval had the greatest rate of change?

1. hour 0 to hour 1
2. hour 1 to hour 2
3. hour 2 to hour 3
4. hour 3 to hour 4

Explanation:

Step1: Calculate rate of change for option 1

Rate of change formula: $\frac{y_2 - y_1}{x_2 - x_1}$. For hour 0 - hour 1: $x_1 = 0,y_1 = 0;x_2 = 1,y_2 = 2.5$. Rate of change $=\frac{2.5 - 0}{1 - 0}=2.5$.

Step2: Calculate rate of change for option 2

For hour 1 - hour 2: $x_1 = 1,y_1 = 2.5;x_2 = 2,y_2 = 4$. Rate of change $=\frac{4 - 2.5}{2 - 1}=1.5$.

Step3: Calculate rate of change for option 3

For hour 2 - hour 3: $x_1 = 2,y_1 = 4;x_2 = 3,y_2 = 4.5$. Rate of change $=\frac{4.5 - 4}{3 - 2}=0.5$.

Step4: Calculate rate of change for option 4

For hour 3 - hour 4: $x_1 = 3,y_1 = 4.5;x_2 = 4,y_2 = 5$. Rate of change $=\frac{5 - 4.5}{4 - 3}=0.5$.

Answer:

1.