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 form of a linear equation

The general form of a linear - equation is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. We can observe from the table that as $x$ (minutes of exercise) increases, $y$ (hours of sleep) also increases. So the slope $m$ should be positive.

Step2: Analyze the slope sign in the options

Options C ($y=-0.058x - 4.138$) and D ($y=-0.058x + 4.138$) have negative slopes, so we can eliminate them.

Step3: Check the y - intercept

We can use the fact that when $x = 0$, $y=b$. Looking at the data, when $x$ is around 30, $y$ is around 6 - 6.5. If we substitute $x = 0$ into option A ($y = 0.058x-4.138$), we get $y=-4.138$ which is not reasonable as the number of hours of sleep cannot be negative. When we substitute $x = 0$ into option B ($y = 0.058x + 4.138$), we get $y = 4.138$. As $x$ increases, the value of $y$ will increase according to the positive - slope relationship.

Answer:

B. $y = 0.058x + 4.138$