which functions have an additive rate of change of 3? choose two correct answers

Explanation:

Step1: Recall the formula for additive rate of change (slope)

The formula for the slope $m$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$.

Step2: Calculate the slope for the table

Let $(x_1,y_1)=(2, - 3)$ and $(x_2,y_2)=(4,-9)$. Then $m=\frac{-9-(-3)}{4 - 2}=\frac{-9 + 3}{2}=\frac{-6}{2}=-3$.

Step3: Calculate slope for a line on a graph

For a line on a graph, pick two points. For a linear - looking graph, if we pick two points $(x_1,y_1)$ and $(x_2,y_2)$ and calculate $\frac{y_2 - y_1}{x_2 - x_1}$. For a non - linear graph, the rate of change is not constant. A linear function has a constant additive rate of change. If we assume two points on a linear graph $(x_1,y_1)$ and $(x_2,y_2)$ and calculate the slope. If the graph is linear and $m = 3$, we check: Let's say we have two points $(x_1,y_1)$ and $(x_2,y_2)$ on a line. If $x_2=x_1 + 1$, then $y_2=y_1+3$ for a slope of 3. We need to visually inspect the graphs. For a linear graph, we can pick two points $(x_1,y_1)$ and $(x_2,y_2)$ and calculate $\frac{y_2 - y_1}{x_2 - x_1}$. If the result is 3, then that function has an additive rate of change of 3.

We assume we have calculated the slopes for all the graphs and tables.

Answer:

We need the actual calculations for each graph and table to give the specific two correct answers. But the general method is to use the slope formula $m=\frac{y_2 - y_1}{x_2 - x_1}$ for tables and linear - looking graphs to find the functions with a slope (additive rate of change) of 3.