in order for the data in the table to represent a linear function with a rate of change of +5, what must be…

Explanation:

Step1: Recall rate - of - change formula

The rate of change (slope) $m$ of a linear function is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$. We know $m = 5$, $x_1=3$, $y_1 = 13$, $x_2=4$, and $y_2=a$.

Step2: Substitute values into formula

$5=\frac{a - 13}{4 - 3}$.

Step3: Solve for $a$

Since $4-3 = 1$, the equation becomes $5=a - 13$. Add 13 to both sides: $a=5 + 13$. So $a = 18$.

Answer:

C. $a = 18$