Question

Ron tracks the time it takes him to mow lawns by writing coordinate points relating x, the time in hours it takes to mow a lawn, and y, the area of land mowed in acres. Two of his points are (3, 1.5) and (5, 2.5). Which statement describes the slope of the line through these two points?

It takes Aaron about 1 hour to mow 2 acres.
Aaron’s rate for mowing lawns is 0.5 acres per hour.
The ratio of acres to time is 5 acres to 3 hours.
The rate to mow a lawn is 0.6 hours per acre.

Answer 1

The statement "The rate to mow a lawn is 0.6 hours per acre" describes the slope of the line through the two points (3, 1.5) and (5, 2.5). The slope represents the rate of change between the two variables, which in this case is the rate at which Aaron mows lawns. The slope is calculated by taking the change in y-coordinates divided by the change in x-coordinates:

slope = (change in y) / (change in x)
= (2.5 - 1.5) / (5 - 3)
= 1 / 2
= 0.5

The slope of the line is 0.5, which means Aaron mows lawns at a rate of 0.5 acres per hour.

Answer 2

Aaron’s rate for mowing lawns is 0.5 acres per hour.

Explanation:

Apply the slope formula to the 2 points to get the slope, which is the y-axis distance divided by the x-axis distance:

`slope=(y_(2)-y_(1))/(x_(2)-x_(1))\\slope=(2.5-1.5)/(5-3)\\slope = (1)/(2)`

The slope suggests that Aaron mows 0.5 acres per hour, since the x-axis represents time and the y-axis represents acres. The third option is the correct answer.