Question

Which of these are solutions to y≤ –4x+2?
(-7,-3)

(0,1)

(-5,4)

(-9,10)

(1,-2)

(2,-10)

Answer 1

To determine if a point is a solution to the inequality y ≤ -4x + 2, we need to substitute the x and y values of each point into the inequality and see if it is true.

1. (-7, -3)
-3 ≤ -4(-7) + 2
-3 ≤ 28 + 2
-3 ≤ 30
This is false, so (-7, -3) is not a solution.

2. (0, 1)
1 ≤ -4(0) + 2
1 ≤ 2
This is true, so (0, 1) is a solution.

3. (-5, 4)
4 ≤ -4(-5) + 2
4 ≤ 20 + 2
4 ≤ 22
This is true, so (-5, 4) is a solution.

4. (-9, 10)
10 ≤ -4(-9) + 2
10 ≤ 36 + 2
10 ≤ 38
This is true, so (-9, 10) is a solution.

5. (1, -2)
-2 ≤ -4(1) + 2
-2 ≤ -2 + 2
-2 ≤ 0
This is true, so (1, -2) is a solution.

6. (2, -10)
-10 ≤ -4(2) + 2
-10 ≤ -8 + 2
-10 ≤ -6
This is false, so (2, -10) is not a solution.

Therefore, the solutions to y ≤ -4x + 2 are (0, 1), (-5, 4), (-9, 10), and (1, -2).