A teacher is assessing the correlation between the number of hours spent studying and the average score on a science test. The table shows the data: Number of hours spent studying
(x) 0 0.5 1 1.5 2 2.5 3 3.5 4
Score on science test
(y) 57 62 67 72 77 82 87 92 97

Part A: Is there any correlation between the number of hours students spent studying and the score on the science test? Justify your answer. (4 points)

Part B: Write a function that best fits the data. (3 points)

Part C: What does the slope and y-intercept of the plot indicate? (3 points)

From the table we see there is a relation between x and y values

Every step change of x = 0.5, every step change of y = 2

This relation is linear. The formula for linear function is:

y = mx + b

Using to pairs of points to get the slope and y-intercept

(0, 60) and (1, 64)

Calculating the slope:

m = (64 - 60)/(1 - 0) = 4/1 = 4

y - intercept is 60 as per point (0, 60)

So the function is

y = 4x + 60

Part A

Yes. Described above

Part B

y = 4x + 60

Part C

Slope is the steepness of the line.

y -intercept is the lowest score with no time spent studying

HOPE I HELPED ! Have a great day :)