Question

which of the points are solutions to the inequality? check all that apply. (-2, -5) (0, -4) (1, 1) (3, 5) (5, 5) the graph shows the inequality y > 2x - 4 with a dashed line and shaded region.

Explanation:

Step1: Check point (-2, -5)

Substitute \(x = -2\), \(y = -5\) into \(y > 2x - 4\):
\(-5 > 2(-2) - 4\)
\(-5 > -4 - 4\)
\(-5 > -8\) (True)

Step2: Check point (0, -4)

Substitute \(x = 0\), \(y = -4\) into \(y > 2x - 4\):
\(-4 > 2(0) - 4\)
\(-4 > -4\) (False, since it's not greater than)

Step3: Check point (1, 1)

Substitute \(x = 1\), \(y = 1\) into \(y > 2x - 4\):
\(1 > 2(1) - 4\)
\(1 > 2 - 4\)
\(1 > -2\) (True)

Step4: Check point (3, 5)

Substitute \(x = 3\), \(y = 5\) into \(y > 2x - 4\):
\(5 > 2(3) - 4\)
\(5 > 6 - 4\)
\(5 > 2\) (True)

Step5: Check point (5, 5)

Substitute \(x = 5\), \(y = 5\) into \(y > 2x - 4\):
\(5 > 2(5) - 4\)
\(5 > 10 - 4\)
\(5 > 6\) (False)

Answer:

\((-2, -5)\), \((1, 1)\), \((3, 5)\)