Question

Sloane believes there is a correlation between the number of texts sent in class and GPA. She collected data and found that the line of best fit for the data can be modeled by the equation y = 4.0 − 0.5x.
Identify and interpret the slope in this scenario.

a. The slope is −4.0. Starting at 0.5, the GPA will decrease by 4.0 for every text sent in class.
b. The slope is −0.5. Starting at 4.0, the GPA will decrease by 0.5 for every text sent in class.
c. The slope is 4.0. Starting at 0.5, the GPA will increase by 4.0 for every text sent in class.
d. The slope is 0.5. Starting at 4.0, the GPA will increase by 0.5 for every text sent in class.

Answer 1

The slope is -.5. Starting at 4

Answer 2

Answer: b. The slope is -0.5. Starting at 4.0, the GPA will decrease by 0.5 for every text sent in class.

Step-by-step explanation:

We know that the equation of a line in intercept form is given by :-

$y=mx+c$, where m is the slope and c is the y-intercept.           (i)

Given : Sloane believes there is a correlation between the number of texts sent in class and GPA. She collected data and found that the line of best fit for the data can be modeled by the equation :-

$y = 4.0-0.5x$

When we compare it to (i), we get

m=-0.5 and c=4.0

It means the slope is -0.5 and the function is starting at 4.0 and the GPA will decrease by 0.5 for every text sent in class (since its negative).