Question

Which system of inequalities does the graph represent? Which test point satisfies both of the inequalities in that system?

Answer 1

Answers + Explanation:

1. Red inequality

First, find the equation of the red line.

You can see that when x goes up by 2, y goes down by 3 so the slope would be -3/2 or -1/5.

Then, the y-intercept is 1.5 so the equation is y = -1.5x + 1.5.

Since you can see the green part is below the red line and the line is solid, the inequality would have a ≤ sign.

The inequality is y ≤ -1.5x + 1.5

2. Blue inequality

Next, find the equation of the blue line.

You can see that when x goes up by 4, y goes down by 3 so the slope of the line would be -3/4 or -0.75.

Next, you can see that the y-intercept is 0.5.

This means that the equation of the line is y = -0.75x + 0.5.

Since the green shaded part is above the blue line and the blue line is solid, the inequality will have a ≥ sign.

It would be y ≥ -0.75x + 0.5

3. Test point

Any point in the green shaded section should work as a test point. For example, you can use (-1, 2)

Plug this into both in equalities:

Red: 2 ≤ -1.5 * -1 + 1.5

2 ≤ 1.5 + 1.5

2 ≤ 3

true

Blue: 2 ≥ -0.75 * -1 + 0.5

2 ≥ 0.75 + 0.5

2 ≥  1.25

true

Both are true so this is correct.