Question

Which equation represents the potential line of best fit for the provided data set?

x y
3 -0.25
5 -1.00
7 -1.50
9 -1.75
11 -2.25
13 -2.25
15 -2.75
17 -3.25
19 -3.50
21 -3.50

a. y=−0.2x=−0.25
b. y=−0.15x−0.5
c. y=−0.2x−0.5
d. y=−0.15x−0.25

Answer 1

Option c, y = -0.2x - 0.5, appears to be a reasonable approximation for the line of best fit for the provided data set, considering the negative trend of the data points and an estimate of the y-intercept based on the values given.

Step-by-step explanation:

To determine which equation best represents the potential line of best fit for the provided data set, we need to look at the pattern of the data points. Given that the values of y decrease as the values of x increase, we are looking for a negative slope. We can estimate the slope by picking two points and calculating the change in y over the change in x (rise over run). Looking at the data, from x=3 to x=21, y changes from -0.25 to -3.5, so the slope is approximately (3.5-0.25)/(21-3) = 3.25/18 = -0.1806, which is close to -0.2 or -0.15. Furthermore, the starting y value when x=3 is -0.25 which can serve as an estimate for the y-intercept. Considering the possible answers and our crude estimates, option c, y = -0.2x - 0.5, appears to be a reasonable approximation for the line of best fit. Without exact calculations or a graphing tool, we cannot be certain, but this would likely be the strongest candidate.