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?
( circ y > 2x + 1 )
( circ y < 2x - 1 )
( circ y geq 2x + 1 )
( circ y leq 2x - 1 )

Explanation:

Step1: Substitute (1,1) into each inequality

Test each option with $x=1, y=1$:

1. For $y>2x+1$: $1>2(1)+1 \implies 1>3$ (False)
2. For $y<2x-1$: $1<2(1)-1 \implies 1<1$ (False)
3. For $y\geq2x+1$: $1\geq2(1)+1 \implies 1\geq3$ (False)
4. For $y\leq2x-1$: $1\leq2(1)-1 \implies 1\leq1$ (True)

Answer:

$y \leq 2x - 1$ (the fourth option)