Question

renee created a scatterplot of time spent training each week (hours) vs. mile time (minutes). the slope of the line of best fit for this scatterplot is -0.5 and the y - intercept is 16. which of the following conclusions can be made? a) with 0 hours of training, renees mile time was 16 minutes. b) with 0 hours of training, renees mile time was 0.5 minutes slower. c) renee started with 16 hours of training. d) with each additional hour spent training, renees mile time decreased by about 0.5 minutes.

Explanation:

Step1: Recall slope - intercept form

The equation of a line in slope - intercept form is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. Here, $m=- 0.5$ and $b = 16$, so the equation is $y=-0.5x + 16$, with $x$ being hours of training and $y$ being mile time.

Step2: Analyze y - intercept

When $x = 0$ (0 hours of training), substituting into the equation $y=-0.5(0)+16$, we get $y = 16$. This means with 0 hours of training, Renee's mile time was 16 minutes.

Step3: Analyze slope

The slope $m=-0.5$ means that for each increase of 1 in $x$ (each additional hour of training), $y$ (mile time) decreases by 0.5.

Answer:

A. With 0 hours of training, Renee's mile time was 16 minutes.
D. With each additional hour spent training, Renee's mile time decreased by about 0.5 minutes.