Question

practice interpreting two - variable linear inequalities. the inequality is $y < 2x + 3$. there is a coordinate grid with the line of the inequality graphed (dashed line). the question is: which of the points are solutions to the inequality? check all that apply. the points are: $(-3, 3)$, $(-2, -2)$, $(-1, 1)$, $(0, 1)$, $(2, 5)$

Explanation:

Step1: Check point (-3, 3)

Substitute \(x = -3\), \(y = 3\) into \(y < 2x + 3\):
\(3 < 2(-3) + 3\)
\(3 < -6 + 3\)
\(3 < -3\) (False)

Step2: Check point (-2, -2)

Substitute \(x = -2\), \(y = -2\) into \(y < 2x + 3\):
\(-2 < 2(-2) + 3\)
\(-2 < -4 + 3\)
\(-2 < -1\) (True)

Step3: Check point (-1, 1)

Substitute \(x = -1\), \(y = 1\) into \(y < 2x + 3\):
\(1 < 2(-1) + 3\)
\(1 < -2 + 3\)
\(1 < 1\) (False, since it’s \(<\), not \(\leq\))

Step4: Check point (0, 1)

Substitute \(x = 0\), \(y = 1\) into \(y < 2x + 3\):
\(1 < 2(0) + 3\)
\(1 < 0 + 3\)
\(1 < 3\) (True)

Step5: Check point (2, 5)

Substitute \(x = 2\), \(y = 5\) into \(y < 2x + 3\):
\(5 < 2(2) + 3\)
\(5 < 4 + 3\)
\(5 < 7\) (True)

Answer:

B. \((-2, -2)\), D. \((0, 1)\), E. \((2, 5)\)

(Note: The original options’ numbering might vary; here, the correct points are \((-2, -2)\), \((0, 1)\), and \((2, 5)\) based on substitution.)