Question

ms. cassidy plotted the point (2, 3) on miguel’s 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.
( circ y < 2x - 1 )
( circ y leq 2x - 4 )
( circ y > 2x - 4 )
( circ y < 2x + 4 )
( circ y < 3.5x - 4 )
( circ 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.

1. For \(y < 2x - 1\):

Substitute \(x = 2\), \(y = 3\): \(3 < 2(2)-1 = 4 - 1 = 3\). But \(3 < 3\) is false.

1. For \(y \leq 2x - 4\):

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

1. For \(y > 2x - 4\):

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

1. For \(y < 2x + 4\):

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

1. For \(y < 3.5x - 4\):

Substitute \(x = 2\), \(y = 3\): \(3 < 3.5(2)-4 = 7 - 4 = 3\). \(3 < 3\) is false.

1. For \(y < 4x - 4\):

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

Answer:

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