Question

using the graphing calculator to include a solution
mr. hernandez plotted the point (1, 1) on han’s graph of ( y leq \frac{1}{2}x + 2 ). he instructed han to add a second inequality to the graph that would include the solution (1, 1).
which equation could miguel write?
( \bigcirc y > 2x + 1 )
( \bigcirc y < 2x - 1 )
( \bigcirc y geq 2x + 1 )
( \bigcirc y leq 2x - 1 )

Explanation:

Step1: Substitute (1,1) into each inequality

For $y > 2x + 1$: $1 > 2(1)+1 \implies 1>3$, false.
For $y < 2x - 1$: $1 < 2(1)-1 \implies 1<1$, false.
For $y \geq 2x + 1$: $1 \geq 2(1)+1 \implies 1\geq3$, false.
For $y \leq 2x - 1$: $1 \leq 2(1)-1 \implies 1\leq1$, true.

Answer:

D. $y \leq 2x - 1$