Question

the equation for the line of best fit is ( y = -\frac{1}{2}x + 45 ). according to the equation, which of these statements is true?
a road with 32 houses per mile would likely have a speed limit of about 30 miles per hour.
a road with 12 houses per mile would likely have a speed limit of about 50 miles per hour.

Explanation:

Step1: Substitute \(x = 32\) into the equation \(y=-\frac{1}{2}x + 45\)

Substitute \(x = 32\) into \(y=-\frac{1}{2}x + 45\). So, \(y=-\frac{1}{2}\times32+45\).
First, calculate \(-\frac{1}{2}\times32=-16\). Then \(y=-16 + 45=29\approx30\).

Step2: Substitute \(x = 12\) into the equation \(y=-\frac{1}{2}x + 45\)

Substitute \(x = 12\) into \(y=-\frac{1}{2}x + 45\). So, \(y=-\frac{1}{2}\times12+45\).
First, calculate \(-\frac{1}{2}\times12=-6\). Then \(y=-6 + 45 = 39
eq50\).

Answer:

A. A road with 32 houses per mile would likely have a speed limit of about 30 miles per hour.