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 $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here $m = 5$, $x_1=3$, $y_1 = 13$, $x_2 = 4$, 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 $5=\frac{a - 13}{1}$, so $a-13=5\times1$, and $a=5 + 13=18$.

Answer:

C. $a = 18$