Question

Dakota 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 = 3.9 − 0.3x.

Identify and interpret the slope in this scenario.

a. The slope is −3.9. Starting at 0.3, the GPA will decrease by 3.9 for every text sent in class.
b. The slope is 3.9. Starting at 0.3, the GPA will increase by 3.9 for every text sent in class.
c. The slope is 0.3. Starting at 3.9, the GPA will increase by 0.3 for every text sent in class.
d. The slope is −0.3. Starting at 3.9, the GPA will decrease by 0.3 for every text sent in class.​

Answer 1

The correct option is d.

Explanation:

The given equation of best fit line is

`y=3.9-0.3x` .... (1)

The slope intercept form of a line is

`y=mx+b` .... (2)

where, m is slope and b is y-intercept or initial value.

From (1) and (2), we get

`m=-0.3`

`b=3.9`

It means the slope is −0.3. Starting at 3.9, the GPA will decrease by 0.3 for every text sent in class.​

Therefore the correct option is d.

Answer 2

d. The slope is −0.3. Starting at 3.9, the GPA will decrease by 0.3 for every text sent in class.​

Explanation:

You can write the equation is the slope intercept form of y=mx+c

where m is the slope and c in the y-axis intercept

write the equation as;

y=mx+c

y= -0.3x+3.9

Here , you have a negative slope which means the GPA will reduce by 0.3 for every text sent in class.

See attached graph to visualize the y-intercept point