Question

joseph drove from his summer home to his place of work. To avoid the road construction, joseph decided to travel the gravel road. After driving 20 minutes, he was 62 miles away from work, and after driving 40 minutes, he was 52 miles away from work. this situation is shown in the graph below. determine the slope of the line and describe what it means in this situation

Answer 1

The slope of the line is -1/2. The slope (rate of change) means that for every 1/2 minutes that Joseph is driving, he has 10 fewer miles remaining to get to work.

In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

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

By substituting the given data points (20, 62) and (40, 52) into the formula for the slope of a line, we have the following;

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

Slope (m) = (52 - 62)/(40 - 20)

Slope (m) = -10/20

Slope (m) = -1/2.