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=(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=(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=(a-26)/(6-4) \\ -3=(a-26)/(2) \\ a-26=-3*2=-6 \\ \therefore \\ a=-6+26 \\ a=20 \end{gathered}`

Therefore, the correct option is the LAST OPTION.