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

Explanation:

Step1: Recall slope - rate of change formula

The additive rate of change (slope) between two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$.

Step2: Analyze graphs

For a linear graph, pick two points. Let's say for a graph with points $(x_1,y_1)$ and $(x_2,y_2)$. Calculate the slope. If the graph is non - linear, the rate of change is not constant.

Step3: Analyze tables

For a table of values with $x$ and $y$ columns, take two pairs of values $(x_1,y_1)$ and $(x_2,y_2)$ and use the slope formula $m = \frac{y_2 - y_1}{x_2 - x_1}$. For the first table with $x$ values $6,4,2,1$ and $y$ values $- 15,-9,-3,9$: Let $(x_1,y_1)=(6,-15)$ and $(x_2,y_2)=(4,-9)$. Then $m=\frac{-9-(-15)}{4 - 6}=\frac{-9 + 15}{-2}=\frac{6}{-2}=-3$. For the second table with $x$ values $4,3,2,1$ and $y$ values $2,-1,-4,-7$: Let $(x_1,y_1)=(4,2)$ and $(x_2,y_2)=(3,-1)$. Then $m=\frac{-1 - 2}{3 - 4}=\frac{-3}{-1}=3$.

Answer:

The table with $x$ values $4,3,2,1$ and $y$ values $2,-1,-4,-7$ has an additive rate of change of 3.