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. 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

Answer:

Slope of this line is given by:

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

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:

$x_1=3, y_1=1.5\\x_2=5, y_2=2.5$

Change in x coordinate = $x_2-x_1=5-3 = 2$

i.e. total time taken is 2 hours.

Change in y coordinate = $y_2-y_1=2.5-1.5 = 1$

i.e. total land mowed taken is 1 acre.

In other words, it takes 2 hours for Aaron to mow 1 acre of land.

So, "option 1)  It takes Aaron about 1 hour to mow 2 acres." is incorrect.

Rate of mowing lawn is the land mowed by Aaron in 1 hour.

Land mowed in 2 hours = 1 acre

Land mowed in 1 hours = $\frac{1}{2}$ acre i.e. 0.5 acre

Also, slope of a line is given as:

$m = \dfrac{y_2-y_1}{x_2-x_1}$

Here $y_2 - y_1 = 1$

$x_2 - x_1 = 2$

As per formula:

$m = \dfrac{1}{2} = 0.5$

So, option 2) Aaron’s rate for mowing lawns is 0.5 acres per hour.

Answer 2

Answer:

B

Step-by-step explanation: