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.