Question

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

Answer 1

The linear equation that best models the relationship between the number of minutes spent exercising and the number of hours slept is y = 0.058x + 4.138. Option a is correct.

Step-by-step explanation:

The number of hours slept at night is related to the number of minutes spent exercising that day.

To determine the linear equation that best models the relationship between x (minutes spent exercising) and y (hours slept), we need to find the slope and y-intercept.

Using the given data, we can calculate the slope by finding the difference in y-values divided by the difference in x-values:

slope = (8.5 - 6.25) / (76 - 30)

= 0.058.

Next, we can substitute the slope value into the equation y = mx + b,

where m represents the slope.

We can choose any point from the given data to find the y-intercept, so let's use the point (30, 6.25).

Substituting the values into the equation, we have

6.25 = 0.058(30) + b.

Solving for b,

b = 4.138.

Therefore, the linear equation that best models the relationship between x and y is y = 0.058x + 4.138. Option a is correct.