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

`y > 2x-4\\y < 2x+4\\y < 4x-4`

Explanation:

We go through every equation and fill in the x and y values to see which ones are true

Option 1:
`y < 2x-1`

`3 < 2(2)-1\\3 < 4-1\\3 < 3`

Three is not less than 3 so this answer is incorrect

Option 2:
`y\leq 2x-4`

`3\leq 2(2)-4\\3\leq 4-4\\3\leq 0`

3 is not less than or equal to zero so this option is incorrect

Option 3:
`y > 2x-4`

`3 > 2(2)-4\\3 > 4-4\\3 > 0`

Three is greater than zero so this answer is correct

Option 4:
`y < 2x+4`

`3 < 2(2)+4\\3 < 4+4\\3 < 8`

Three is less than eight so this answer is correct

Option 5:
`y < 3.5x-4`

`3 < 3.5(2)-4\\3 < 7-4\\3 < 3`

Three is not less than three so this answer is incorrect

Option 6:
`y < 4x-4`

`3 < 4(2)-4\\3 < 8-4\\3 < 4`

Three is less than 4 so this answer is correct

Hope this helps please let me know if you have further questions