Q4. - Algebra 1

Question

Find the rate of change for the linear function represented in the table.

 

Hours Worked	1	2	3	4
Money Earned(\()	5.50	11.00	16.50	22.00

 

F increase \)6.50/h

G increase \(5.50/h

H decrease \)5.50/h

J decrease $6.50/h

Step-by-Step Solution

Answer

The rate of change for the linear function represented in the table is option G increase $5.50/h.

Step 1. State the concept of rate of change of linear function.

The rate of change for a linear function is the slope, the rise over run, or the change in y over the change in x. The slope can be calculated from two points in a table.

The rate of change increases if the slope is positive and decreases if the slope is negative.

Step 2. State the concept of slope of a linear function.

The slope $\left(m\right)$ of a linear function having two points $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ is given as

Slope $\left(m\right)=\frac{y_2-y_1}{x_2-x_1}$.

From the table take any two points as $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$.

Take $\left(x_1,y_1\right)=\left(1,5.50\right)$ and $\left(x_2,y_2\right)=\left(2,11.00\right)$

Step 3. Calculate the rate of change.

The rate of change is calculated as follows.

$$\begin{gathered} \text{Rate of change = slope} \\ =\frac{y_2-y_1}{x_2-x_1} \\ =\frac{11.00-5.50}{2-1} \\ =\frac{5.50}{1} \\ =5.50 \end{gathered}$$

The rate of change is 5.50 and is positive.

 

Therefore, the rate of change of the given linear function increases at the rate $\text{\$5.50/h}$.

Hence, option G is correct.