Answer:
- If a student studies for 6 hours, they will receive a grade of about 100.
- In general, the longer time spent studying, the higher the student's grade.
Step-by-step explanation:
Given
See attachment for plot
Required
Select all correct options
First, we determine the equation of best fit.
Pick two corresponding points on the plot
[tex](x_1,y_1) = (2,70)[/tex]
[tex](x_2,y_2) = (4,85)[/tex]
Calculate slope (m)
[tex]m = \frac{y_2 - y_1}{x_2 -x_1}[/tex]
[tex]m = \frac{85 - 70}{4-2}[/tex]
[tex]m = \frac{15}{2}[/tex]
[tex]m = 7.5[/tex]
The equation is then calculated as:
[tex]y = m(x - x_1) + y_1[/tex]
This gives:
[tex]y = 7.5(x - 2) + 70[/tex]
[tex]y = 7.5x - 15 + 70[/tex]
[tex]y = 7.5x +55[/tex]
The above represents the line of best fit.
By comparison, (a) is incorrect
We calculate the slope to be:
[tex]m = 7.5[/tex]
Since the slope is positive, then the relationship is positive (b is incorrect)
Also, the positive slope implies that, as x increases, y also increase.
Hence, (d) is correct.
For (c), we substitute 6 for x in the calculated equation of best fit
[tex]y = 7.5x +55[/tex]
[tex]y = 7.5 * 6 + 55[/tex]
[tex]y = 45 + 55[/tex]
[tex]y = 100[/tex]
This shows that (c) is true because 6 hours of study gives a grade of 100
