in order for the data in the table to represent a linear function with a rate of change of -8, what must be…

Answer:

C. $a = 19$

Explanation:

Step1: Recall slope formula

The slope (rate of change) formula for a linear function is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Given $m=- 8$.

Step2: Use two - point pairs

Let $(x_1,y_1)=(10,27)$ and $(x_2,y_2)=(11,a)$ and $(x_3,y_3)=(12,11)$. First, using $(x_1,y_1)$ and $(x_2,y_2)$: $m=\frac{a - 27}{11 - 10}$. Since $m=-8$, we have $\frac{a - 27}{1}=-8$.

Step3: Solve for $a$

$a-27=-8$. Add 27 to both sides: $a=-8 + 27=19$.