Question

The anwsers are A.(0,-1) B.(-2,3) C(-4,0) D(0,-4)

Answer 1

Answer:   D.   (0, -4)

=========================================================

Explanation:

If you solve for y, you would get $y \le -\frac{1}{4}x-2$. The less than or equal to sign shows we shade below the solid boundary line.

Of the four answer choices mentioned, only (0,-4) is in the shaded region. So this is the only solution.

If we plugged the coordinates into the inequality, we get a true statement as shown below

$x + 4y \le -8\\\\0 + 4(-4) \le -8\\\\-16 \le -8$

This is a true statement because -16 is to the left of -8 on the number line. So -16 is smaller.

In contrast, if we tried something like (x,y) = (0,-1), then we see...

$x + 4y \le -8\\\\0 + 4(-1) \le -8\\\\-4 \le -8$

Which is not true because -4 is actually larger than -8. Use a number line to see this. So (0,-1) is not a solution. The same can be said about (-2,3) and (-4,0) also.