Question

1. betty makes a scatter plot representing the total time she exercises as a function of the distance she runs. use the trendline y = 7.5x + 10 from the graph below to estimate how long it will take to run 7 miles.

Explanation:

Step1: Substitute \(x = 7\) into the equation

We are given the trendline equation \(y = 7.5x+10\). Here, \(x\) represents the distance (in miles) and \(y\) represents the total time (in minutes). We want to find the time \(y\) when \(x = 7\) (since the distance is 7 miles).
Substitute \(x = 7\) into the equation: \(y=7.5\times7 + 10\).

Step2: Calculate \(7.5\times7\)

Using multiplication, \(7.5\times7=(7 + 0.5)\times7=7\times7+0.5\times7 = 49+3.5=52.5\).
So the equation becomes \(y = 52.5+10\).

Step3: Calculate the sum

Add \(52.5\) and \(10\): \(y=52.5 + 10=62.5\).

Answer:

\(62.5\) minutes.