Question

the solutions to the inequality ( y leq 2x - 4 ) are shaded on the graph. which point is a solution?
( \bigcirc ) ( (-1, 1) )
( \bigcirc ) ( (1, -1) )
( \bigcirc ) ( (3, 2) )
( \bigcirc ) ( (2, 3) )

Explanation:

Step1: Test point (-1,1)

Substitute \(x = -1\), \(y = 1\) into \(y\leq2x - 4\):
\(1\leq2(-1)-4\)
\(1\leq - 2 - 4\)
\(1\leq - 6\) (False)

Step2: Test point (1,-1)

Substitute \(x = 1\), \(y = -1\) into \(y\leq2x - 4\):
\(-1\leq2(1)-4\)
\(-1\leq2 - 4\)
\(-1\leq - 2\) (False)

Step3: Test point (3,2)

Substitute \(x = 3\), \(y = 2\) into \(y\leq2x - 4\):
\(2\leq2(3)-4\)
\(2\leq6 - 4\)
\(2\leq2\) (True)

Step4: Test point (2,3)

Substitute \(x = 2\), \(y = 3\) into \(y\leq2x - 4\):
\(3\leq2(2)-4\)
\(3\leq4 - 4\)
\(3\leq0\) (False)

Answer:

(3, 2)