Question

select the correct answer.
wayne is recording the number of hours he sleeps over different periods of time. the table provided shows the number of hours wayne sleeps during the respective amount of days.

number of days	hours of sleep
6	30
9	45
12	60
15	75

what is the rate of change of waynes hours of sleep with respect to each day?

Explanation:

Step1: Recall rate of change formula

The rate of change (slope) between two points \((x_1,y_1)\) and \((x_2,y_2)\) is given by \(\frac{y_2 - y_1}{x_2 - x_1}\). We can use any two points from the table. Let's take the first two points: \((3,15)\) and \((6,30)\).

Step2: Calculate the rate of change

Substitute \(x_1 = 3\), \(y_1 = 15\), \(x_2 = 6\), \(y_2 = 30\) into the formula: \(\frac{30 - 15}{6 - 3}=\frac{15}{3}=5\). We can check with another pair, say \((6,30)\) and \((9,45)\): \(\frac{45 - 30}{9 - 6}=\frac{15}{3}=5\). So the rate of change is consistent.

Answer:

5