Question

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

Answer 1

By definition, the Rate of change is also called "Slope".

The slope of a line can be found dividing the difference between the y-coordinates of two points, by the difference between the x-coordinate of those points:

`m=(y_2-y_1)/(x_2-x_1)`

In this case you know that:

`m=-8`

Knowing the following point on the line:

`\mleft(10,27\mright);(11,a)`

You can set up the following (substituting the slope and the coordinates of those point into the formula)

`-8=(27-a)/(10-11)`

Now you can solve for "a":

`\begin{gathered} (-8)(-1)=27-a \\ 8-27=a \\ -19=a \\ a=19 \end{gathered}`

The answer is: Third option.