For part A. One way to know if there is a correlation between the data is to graph the data set, like this
Then, as can you see the data presents a positive linear correlation.
For part B. You can take the coordinates of two points and find the slope of the line using the formula
[tex]\begin{gathered} m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ \text{ Where m is the slope of the line and} \\ (x_1,y_1)\text{ and }(x_2,y_2)\text{ are two points through which the line passes} \end{gathered}[/tex]
If you take
[tex]\begin{gathered} (x_1,y_1)=(1,67) \\ (x_2,y_2)=(3,87) \\ \text{ You have} \\ m=\frac{87-67}{3-1} \\ m=\frac{20}{2} \\ m=10 \end{gathered}[/tex]
Now, using the slope formula, you can find the equation of the line in its slope-intercept form
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-67=10(x-1) \\ y-67=10x-10 \\ \text{ Add 67 on both sides of the equation} \\ y-67+67=10x-10+67 \\ y=10x+57 \end{gathered}[/tex]
Therefore, the function that best fits the data is
[tex]y=10x+57[/tex]
For part C. The slope of the plot is 10 and indicates that for every hour students spend time studying, they get 10 more points on the science test.
The y-intercept of the plot is 57 and indicates that if students study 0 hours for the science test, they will obtain 57 points as a grade.
