The graph of the line 5x − 2y = 8 is shown. Which THREE ordered pairs are in the solution set of the inequality 5x − 2y ≥ 8? (−2, −4) (−1, −10) (0, −2) (1, −4) (2, 0)

Answer 1

You are given a graph of the line 5x – 2y = 8, which should have x-intercept (1.6,0) and y-intercept (0,–4).

For the solution set of the inequality 5x – 2y ≥ 8 you need to figure out which side of the line contains the solution set. There are several ways to do this, but I think the easiest (and quickest) way is to

test the point (0, 0) and see whether or not it's in the solution set.

So we take the inequality 5x – 2y ≥ 8 and plug in x = y = 0 and get 5(0) – 2(0) ≥ 8 which is false because 0 is not greater than or equal to 8.

So the solution set will be to the right of the line 5x – 2y = 8 which does not contain the point (0, 0).

If we plot the five points on the given graph we see that (–2, –4) and (0, –2) are to the left of the line and therefore are NOT in the solution set of the inequality.

The other three points (–1, –10), (1, –4), and (2, 0) are to the right of the line and therefore ARE in the solution set of the inequality.

Answer 2

5x − 2y ≥ 8? (−2, −4) (−1, −10) (0, −2) (1, −4) (2, 0)

You can see which points make the equation true.

5(-2)-2(-4) ≥ 8

-10+8 ≥ 8

-2 ≥ 8 NO

5(-1)-2(-10) ≥ 8

-5+20 ≥ 8

15 ≥ 8 YES

5(0)-2(-2) ≥ 8

0+4 ≥ 8

4 ≥ 8 NO

5(1)-2(-4) ≥ 8

5+8 ≥ 8

13 ≥ 8 YES

5(2)-2(0) ≥ 8

10+0 ≥ 8

10 ≥ 8 YES