Question

Please Help Me With This Math Problem

Answer 1

Yes the relationship is linear and given by:

`y+2=-(5)/(4) \,(x+9)` (first option of your list)

Explanation:

Yes, it is a linear expression. As we did in previous exercises, we calculate the difference between consecutive y values of the table, and write down the answers we get:

-7-(-2) = -7+2 = -5

-12-(-7) = -12 +7 = -5

-17 - (-12) = -17 + 12 = -5

We notice that all of them give "-5"

Now we evaluate the difference between consecutive x-values in a similar fashion:

-5 -(-9) = -5+9 = 4

-1-(-5) = -1+5 = 4

3-(-1) = 3+1 = 4

We see that they all give 4 as the difference.

That means that the rate of change
`(y_2-y_1)/(x_2-x_1) =(y_3-y_2)/(x_3-x_2)=(y_4-y_3)/(x_4-x_3)=(-5)/(4)`

This means that the slope (rate of change) of the line is "-5/4"

We can now use the general point-slope form to write the equation of the line, using the first pair of the table as our selected point, and using "-5/4" for the slope:

`y-y_0=m\,(x-x_0)\\y-(-2)=-(5)/(4) \,(x-(-9))\\y+2=-(5)/(4) \,(x+9)`

which is the first expression listed among your possible answer choices.