Aaron 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.
Answers
Using the slope concept, it is found that the correct option is:
Aaron’s rate for mowing lawns is 0.5 acres per hour.
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A linear function has the following format:
y = mx + by=mx+b
The slope is m, which is the rate of change, that is, by how much the output y changes when the input changes by 1.
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In this question, the input is the time in hours and the output is the area of land mowed, thus the slope represented the rate of area mowed per hour.
Two points, (3, 1.5) and (5, 2.5). The slope is change in y divided by the change in x, thus:
m = \frac{2.5 - 1.5}{5 - 3} = \frac{1}{2} = 0.5m=
5−3
2.5−1.5
=
2
1
=0.5
Thus, the correct option is:
Aaron’s rate for mowing lawns is 0.5 acres per hour.
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