Question

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.
• aarons 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.

Explanation:

Step1: Recall slope formula

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \).

Step2: Identify coordinates

Here, \( x_1 = 3\), \( y_1 = 1.5\), \( x_2 = 5\), \( y_2 = 2.5 \).

Step3: Calculate slope

Substitute into the formula: \( m=\frac{2.5 - 1.5}{5 - 3}=\frac{1}{2}=0.5 \).
This slope represents the rate (acres per hour) since \( y \) is area (acres) and \( x \) is time (hours).

Answer:

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