Question

Mrs. Jackson gives the table below to her students.y2623aX4556In order for the function to be linear, what must a beand why?O a = 22 because the rate of change is 1.a = 20 because the rate of change is 3.O a = 22 because the rate of change is -1.O a= 20 because the rate of change is -3.m

Answer 1

The table in the question is provided.

A linear function is written in the form:

$y=mx+b$

where m is the slope and b is the y-intercept.

The slope is calculated using the formula:

$m=\frac{y_2-y_1}{x_2-x_1}$

If we use the first two points, we can calculate the slope as follows:

$\begin{gathered} (x_1,y_1)=(4,26) \\ (x_2,y_2)=(5,23) \\ \therefore \\ m=\frac{23-26}{5-4} \\ m=-3 \end{gathered}$

Therefore, for us to solve for a, we can use the slope formula but the slope must be -3:

$\begin{gathered} (x_1,y_1)=(4,26) \\ (x_2,y_2)=(6,a) \\ \therefore \\ -3=\frac{a-26}{6-4} \\ -3=\frac{a-26}{2} \\ a-26=-3\times2=-6 \\ \therefore \\ a=-6+26 \\ a=20 \end{gathered}$

Therefore, the correct option is the LAST OPTION.