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?

Answer:

the answer is A

Step-by-step explanation:

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Final answer:

The linear equation that best models the relationship between the number of minutes spent exercising and the number of hours slept is y = 0.04643x + 4.607.

Explanation:

The relationship between the number of minutes spent exercising, x, and the number of hours slept, y, can be modeled by a linear equation. To find the equation, we can use the formula for a line, y = mx + b, where m is the slope and b is the y-intercept.

To find the slope, we need to calculate the difference in y-values divided by the difference in x-values for any two points on the line. Let's take the first and last points: (30, 6.25) and (76, 8.5).

Slope (m) = (8.5 - 6.25) / (76 - 30) = 0.04643

Next, to find the y-intercept, we can substitute one point and the slope into the equation and solve for b. Let's use point (30, 6.25):

6.25 = 0.04643 * 30 + b

b = 4.607

Therefore, the linear equation that best models the relationship between x and y is y = 0.04643x + 4.607.

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