Question

The table shows a linear function. What is the rate of change?

Hours
Pay
1
18
1.5
23
2
28
2.5
33
3
38

Answer 1

The rate of change for the given linear function is 10.

The table represents a linear function. To find the rate of change, we need to determine the slope of the function. The slope is calculated by finding the difference in the values of the dependent variable (Pay) divided by the difference in the values of the independent variable (Hours).

Let's take the first two data points: (1, 18) and (1.5, 23).

The difference in Pay is 23 - 18 = 5, and the difference in Hours is 1.5 - 1 = 0.5.

Therefore, the rate of change or slope between these two points is 5/0.5 = 10.

The rate of change in a linear function is the slope of the line represented by the function. To calculate the rate of change from the table provided, you find the difference in the pay (which is the dependent variable) for a corresponding difference in the hours (which is the independent variable). Using any two points from the table, for example, (1, 18) and (2, 28), the rate of change (slope) is calculated as the change in pay divided by the change in hours: (28 - 18) / (2 - 1) = 10 / 1 = 10. Therefore, the rate of change is $10 per hour. This indicates that for every additional hour worked, the pay increases by 10.

Answer 2

rate of change = 5

Explanation:

the slope m gives the measure of the rate of change of the function

calculate the slope m using the slope formula

m =
`\frac{y_{2-y_(1) } }{x_{2-x_(1) } }`

with (x₁, y₁ ) = (3, 38) and (x₂, y₂ ) = (1, 18) ← 2 ordered pairs from the table

m =
`(18-38)/(1-3)` =
`(-20)/(-2)` = 5

then rate of change = 5