Question

The graph represents y = −1/4 x − 3. Which coordinate pair is NOT a solution for the equation? Responses A(−8, −1) (−8, −1) B(0, −3) (0, −3) C(−2, −4) (−2, −4) D(4, −4) (4, −4) Question 2

Answer 1

The equation given in the problem is shown below:

`y=-(1)/(4) x-3`

Here are the answer choices:

a) (-8,-1)

b) (0,-3)

c) (-2,-4)

d) (4,-4)

We are asked to choose the coordinate pair that is NOT a solution, so let's just test each option!

To test answer choice "a", plug in
`x=-8` and
`y=-1` into the original equation, then simplify:

Plug in values:
`-1=-(1)/(4) (-8)-3`

Multiply:
`-1=2-3`

Subtract:
`-1=-1`

Notice that we now have a true expression, therefore option "a" IS A SOLUTION, and is thus not the correct answer.

Repeat for option "b" (0, -3):

Plug in values:
`-3=-(1)/(4)(0)-3`

Multiply:
`-3=-3`

Notice that we now have a true expression, therefore option "b" IS A SOLUTION, and is thus not the correct answer.

Repeat for option "c" (-2, -4):

Plug in values:
`-4=-(1)/(4)(-2)-3`

Multiply:
`-4=(1)/(2) -3`

Subtract:
`-4=-(5)/(2)`

Notice that we now have a false expression, therefore option "c" IS NOT SOLUTION, and is thus the correct answer.

To ensure we have the right option, check option "d" as well (4, -4):

Plug in values:
`-4=-(1)/(4) (4)-3`

Multiply:
`-4=-1-3`

Subtract:
`-4=-4`

Notice that we now have a false expression, therefore option "d" IS A SOLUTION, and is thus not the correct answer.

Notice that we have now checked all possible options and only option "c" was evaluated as a false expression, therefore option C is the correct choice in regard to this question.

Let me know if you have any questions!