To determine the slope of the line that goes through the points (3, 1.5) and (5, 2.5), we can use the formula for the slope (m) between two points \((x_1, y_1)\) and \((x_2, y_2)\):
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
For the points given:
\((x_1, y_1) = (3, 1.5)\)
\((x_2, y_2) = (5, 2.5)\)
Now we can plug these values into the slope formula:
\[ m = \frac{2.5 - 1.5}{5 - 3} = \frac{1}{2} \]
This means that the slope of the line is 0.5, which indicates that Aaron mows 0.5 acres for every hour he spends mowing.
Now, let's analyze each statement given:
-
It takes Aaron about 1 hour to mow 2 acres.
- This is incorrect; the slope indicates he mows 0.5 acres in 1 hour, not 2 acres.
-
Aaron’s rate for mowing lawns is 0.5 acres per hour.
- This is correct; it matches the slope we calculated.
-
The ratio of acres to time is 5 acres to 3 hours.
- This is incorrect since that would imply Aaron mows 5/3 = 1.67 acres per hour.
-
The rate to mow a lawn is 0.6 hours per acre.
- This is incorrect; to find the time per acre, you can take the reciprocal of the slope (1 / 0.5 = 2 hours per acre).
Therefore, the correct statement that describes the slope of the line through the two points is:
Aaron’s rate for mowing lawns is 0.5 acres per hour.