Question

Find the rate of change represented in each table or graph.

x	y
1	$-3$
0	$-3$
4	$-3$
12	$-3$

Short answer

The rate of change represented in the given table is0.

Step-by-step solution

Step 1. Write the formula to find the rate of change.

The Formula to find the rate of change (m) when two points are $\left(x_1,y_1\right)$and $\left(x_2,y_2\right)$is:

$m=\frac{y_2-y_1}{x_2-x_1}$

Step 2. Find the rate of change represented in the given table.

The rate of change $\left(m_1\right)$when the two points are width="128" height="25" role="math">x1,y1=−2,−3and $\left(x_2,y_2\right)=\left(0,-3\right)$is:

$$\begin{gathered} m_1=\frac{y_2-y_1}{x_2-x_1} \\ =\frac{-3-\left(-3\right)}{0-\left(-2\right)} \\ =\frac{-3+3}{2} \\ =\frac{0}{2} \\ =0 \end{gathered}$$

The rate of change $\left(m_2\right)$when the two points are$\left(x_3,y_3\right)=\left(4,-3\right)$and$\left(x_4,y_4\right)=\left(12,-3\right)$is:

$$\begin{gathered} m_2=\frac{y_4-y_3}{x_4-x_3} \\ =\frac{-3-\left(-3\right)}{12-4} \\ =\frac{-3+3}{8} \\ =\frac{0}{8} \\ =0 \end{gathered}$$

Therefore, it can be noticed that the rate of change calculated from any of the two points given in the table is same and is equal to 0.

Therefore, the rate of change represented in the given table is 0.