Question

ms. cassidy plotted the point (2, 3) on miguels graph of y < 2x - 4. she instructed him to change one number or one symbol in his inequality so that the point (2, 3) can be included in the solution set. which equations might miguel write? check all that apply. y < 2x - 1; y ≤ 2x - 4; y > 2x - 4; y < 2x + 4; y < 3.5x - 4; y < 4x - 4

Explanation:

To determine which inequalities include the point \((2, 3)\), we substitute \(x = 2\) and \(y = 3\) into each inequality and check if the statement is true.

Step 1: Check \(y < 2x - 1\)

Substitute \(x = 2\), \(y = 3\):
\(3 < 2(2) - 1\)
\(3 < 4 - 1\)
\(3 < 3\) → False (since \(3\) is not less than \(3\)).

Step 2: Check \(y \leq 2x - 4\)

Substitute \(x = 2\), \(y = 3\):
\(3 \leq 2(2) - 4\)
\(3 \leq 4 - 4\)
\(3 \leq 0\) → False.

Step 3: Check \(y > 2x - 4\)

Substitute \(x = 2\), \(y = 3\):
\(3 > 2(2) - 4\)
\(3 > 4 - 4\)
\(3 > 0\) → True.

Step 4: Check \(y < 2x + 4\)

Substitute \(x = 2\), \(y = 3\):
\(3 < 2(2) + 4\)
\(3 < 4 + 4\)
\(3 < 8\) → True.

Step 5: Check \(y < 3.5x - 4\)

Substitute \(x = 2\), \(y = 3\):
\(3 < 3.5(2) - 4\)
\(3 < 7 - 4\)
\(3 < 3\) → False (since \(3\) is not less than \(3\)).

Step 6: Check \(y < 4x - 4\)

Substitute \(x = 2\), \(y = 3\):
\(3 < 4(2) - 4\)
\(3 < 8 - 4\)
\(3 < 4\) → True.

Answer:

• \(y > 2x - 4\)
• \(y < 2x + 4\)
• \(y < 4x - 4\)