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: Recall the slope - intercept form

The linear equation is of the form $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. We can use the general trend of the data to estimate the slope. As $x$ (minutes of exercise) increases, $y$ (hours of sleep) generally increases, so the slope $m>0$.

Step2: Eliminate wrong - sign slope options

Options A and B have negative slopes ($m=- 0.058$), so we can eliminate them since our data shows a positive correlation between $x$ and $y$.

Step3: Consider the y - intercept

We can use the fact that when $x = 0$, $y$ should be a reasonable non - negative value for the number of hours of sleep. If we consider the equation $y=mx + b$, when $x = 0$, $y=b$. For option D, if $x = 0$, $y=-4.138$ which is not a valid number of hours of sleep. For option C, when $x = 0$, $y = 4.138$ which is a reasonable non - negative value for the base number of hours of sleep when no exercise is done.

Answer:

C. $y = 0.058x+4.138$