Question

On a coordinate plane, a solid straight line has a positive slope and goes through (negative 4, 0) and (0, 2). Everything below the line is shaded. A point is shown at (1, 1).
Mr. Hernandez plotted the point (1, 1) on Han’s graph of y ≤ One-halfx + 2. He instructed Han to add a second inequality to the graph that would include the solution (1, 1).

Which equation could Miguel write?

y > 2x + 1
y < 2x – 1
y ≥ 2x + 1
y ≤ 2x – 1

Answer 1

Test each inequality with the point (1, 1):

- y > 2x + 1: 1 > 3 → false
- y < 2x – 1: 1 < 1 → false
- y ≥ 2x + 1: 1 ≥ 3 → false
- y ≤ 2x – 1: 1 ≤ 1 → true

So the correct choice is y ≤ 2x – 1.