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.

On a coordinate plane, a dashed straight line with positive slope goes through (1, negative 2) and (4, 4). Everything to the right of the line is shaded. Point (2, 3) is also shown.
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

Answer 1

The point (2, 3) is on the line y = 2x - 4, so the inequality must be changed to make the point a solution. The only way to do this is to make the inequality less strict.

* y < 2x - 1 is not a solution, because the point (2, 3) is below the line y = 2x - 1.

* y ≤ 2x - 4 is a solution, because the point (2, 3) is on the line y = 2x - 4.

* y > 2x - 4 is not a solution, because the point (2, 3) is below the line y = 2x - 4.

* y < 2x + 4 is not a solution, because the point (2, 3) is below the line y = 2x + 4.

* y < 3.5x - 4 is not a solution, because the point (2, 3) is below the line y = 3.5x - 4.

* y < 4x - 4 is not a solution, because the point (2, 3) is below the line y = 4x - 4.

Therefore, the only equation that Miguel could write is y ≤ 2x - 4.

So the answer is **y ≤ 2x – 4**.