Question

The table shows the number of miles that Teddy has been running over the past 10 weeks.Weeks: 1, 3, 4, 7, 10Miles: 13,19,22,31,40The number of miles that he runs per week can be represented as a linear function.What is the slope? What does the slope represent in the context of tje problem.

Answer 1

Slope:

$m=\frac{y_2-y_1}{x_2-x_1}$

At any point :

$(x_1,y_1)=(1,13)$

and second point:

$(x_2,y_2)_{}=(3,19)$

so slope is:

$\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{19-13}{3-1} \\ m=\frac{6}{2} \\ m=3 \end{gathered}$

so slope of function is 3.

and slope represent the unit change of x then independent variable will result in a change in y by the amount of slope that mean after the some weeks how to distance change is define by slope and slope represent the increasing running distance by Teddy with the weeks.