carol is cross - country skiing. the table shows the distance she traveled after various numbers of minutes…

carol is cross - country skiing. the table shows the distance she traveled after various numbers of minutes. what is the rate of change?\ndistance carol traveled while cross - country skiing\n|minutes|distance traveled (miles)|\n|----|----|\n|2|$\frac{1}{6}$|\n|3|$\frac{17}{48}$|\n|4|$\frac{13}{24}$|\n|5|$\frac{35}{48}$|\n|6|$\frac{11}{12}$|

carol is cross - country skiing. the table shows the distance she traveled after various numbers of minutes. what is the rate of change?\ndistance carol traveled while cross - country skiing\n|minutes|distance traveled (miles)|\n|----|----|\n|2|$\frac{1}{6}$|\n|3|$\frac{17}{48}$|\n|4|$\frac{13}{24}$|\n|5|$\frac{35}{48}$|\n|6|$\frac{11}{12}$|

Answer

Explanation:

Step1: Recall rate - of - change formula

The rate of change (slope) between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$. We can choose any two points from the table. Let's take the first two points: $(x_1 = 2,y_1=\frac{1}{6})$ and $(x_2 = 3,y_2=\frac{17}{48})$.

Step2: Substitute values into formula

$m=\frac{\frac{17}{48}-\frac{1}{6}}{3 - 2}$. First, find a common denominator for the numerator. The common denominator of 48 and 6 is 48. So $\frac{1}{6}=\frac{8}{48}$. Then $\frac{17}{48}-\frac{8}{48}=\frac{17 - 8}{48}=\frac{9}{48}=\frac{3}{16}$. And $3 - 2=1$.

Answer:

$\frac{3}{16}$ miles per minute