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.
y < 2x – 1
y ≤ 2x – 4
y > 2x – 4
y < 2x + 4
y < 3.5x – 4
y < 4x – 4

Answer 1

Ms. Cassidy instructed Miguel to change one sign of the graph of y < 2x – 4 so that point (2, 3) can be included in the solution set.

To check which of the given options might Miguel write we check the inequality that holds true for the point (2,3).Substituting x=2 ,y=3 we have:

1) y < 2x – 1

3<2(2)-1

3<3  Not True.

2)y ≤ 2x – 4

3≤ 2(2) -4

3≤ 0  .Not true.

3) y > 2x – 4

3> 2(2)-4

3> 0   True.

4) y < 2x + 4

3<2(2)+4

3<8   True

5) .y < 3.5x – 4

3< 3.5(2)-4

3<3  Not true

6) y < 4x – 4

3<4(2)-4

3<4   True.

Options 3 ,4 ,6 holds true for the point (2,3)

Answer 2

Its just a matter of subbing in (2,3) into each answer choice...and if it is correct, then it is a solution

answers are :
y > 2x - 4
y < 2x + 4
y < 4x - 4