Question

select the correct answer. the number of hours slept at night is related to the number of minutes spent exercising that day. a collection of data on the number of minutes spent exercising, x, and the number of hours slept, y, is shown in the table. x 30 37 40 45 52 55 61 65 71 76 y 6.25 6 6.5 7 6.5 7.25 7.5 8 8.65 8.5 which linear equation best models the relationship between x and y? a. y = 0.058x - 4.138 b. y = -0.058x + 4.138 c. y = -0.058x - 4.138 d. y = 0.058x + 4.138

Explanation:

Step1: Observe the trend

As \(x\) (exercise - minutes) increases, \(y\) (sleep - hours) generally increases, so the slope of the linear equation should be positive. This eliminates options B and C which have negative slopes.

Step2: Use a point - slope check

Let's take a point, say \((x = 30,y = 6.25)\).
For option A: \(y=0.058x - 4.138\), substituting \(x = 30\) gives \(y=0.058\times30-4.138=1.74 - 4.138=- 2.398
eq6.25\).
For option D: \(y = 0.058x+4.138\), substituting \(x = 30\) gives \(y=0.058\times30 + 4.138=1.74+4.138 = 5.878\approx6.25\) (allowing for some approximation in real - world data).

Answer:

D. \(y = 0.058x + 4.138\)