Answer:
Slope of this line is given by:
<em>Aaron’s rate for mowing lawns is 0.5 acres per hour</em>
Step-by-step explanation:
It is given that time is tracked by Aaron related to x coordinate.
and the area of land mowed in acres is related to y coordinate.
Two of his points are given as:
(3, 1.5) and (5,2.5)
We know that the coordinates are represented in the form of (x,y)
i.e. first coordinate represents x coordinate and
second coordinate represents y coordinate.
So, it can be observed that:
![x_1=3, y_1=1.5\\x_2=5, y_2=2.5](https://tex.z-dn.net/?f=x_1%3D3%2C%20y_1%3D1.5%5C%5Cx_2%3D5%2C%20y_2%3D2.5)
Change in x coordinate = ![x_2-x_1=5-3 = 2](https://tex.z-dn.net/?f=x_2-x_1%3D5-3%20%3D%202)
i.e. total time taken is 2 hours.
Change in y coordinate = ![y_2-y_1=2.5-1.5 = 1](https://tex.z-dn.net/?f=y_2-y_1%3D2.5-1.5%20%3D%201)
i.e. total land mowed taken is 1 acre.
In other words, <em>it takes 2 hours for Aaron to mow 1 acre of land.</em>
So, "option 1) It takes Aaron about 1 hour to mow 2 acres." is incorrect.
<u>Rate of mowing</u> lawn is the <em>land mowed by Aaron in 1 hour</em>.
Land mowed in 2 hours = 1 acre
Land mowed in 1 hours =
acre i.e. 0.5 acre
Also, slope of a line is given as:
![m = \dfrac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=m%20%3D%20%5Cdfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
Here ![y_2 - y_1 = 1](https://tex.z-dn.net/?f=y_2%20-%20y_1%20%3D%201)
![x_2 - x_1 = 2](https://tex.z-dn.net/?f=x_2%20-%20x_1%20%3D%202)
As per formula:
![m = \dfrac{1}{2} = 0.5](https://tex.z-dn.net/?f=m%20%3D%20%5Cdfrac%7B1%7D%7B2%7D%20%3D%200.5)
So, option 2) Aaron’s rate for mowing lawns is 0.5 acres per hour.