using the graphing calculator to include a solution\nmr. hernandez plotted the point (1, 1) on hans graph of…

using the graphing calculator to include a solution\nmr. hernandez plotted the point (1, 1) on hans graph of $yleq\frac{1}{2}x + 2$. he instructed han to add a second inequality to the graph that would include the solution (1, 1). which equation could miguel write?\n$y>2x + 1$\n$y<2x - 1$\n$ygeq2x + 1$\n$yleq2x - 1$

using the graphing calculator to include a solution\nmr. hernandez plotted the point (1, 1) on hans graph of $yleq\frac{1}{2}x + 2$. he instructed han to add a second inequality to the graph that would include the solution (1, 1). which equation could miguel write?\n$y>2x + 1$\n$y<2x - 1$\n$ygeq2x + 1$\n$yleq2x - 1$

Answer

Answer:

D. $y \le 2x - 1$

Explanation:

Step1: Verify the first inequality for point (1, 1).

The first inequality is $y \le \frac{1}{2}x + 2$. Substitute $x=1$ and $y=1$: $1 \le \frac{1}{2}(1) + 2$ $1 \le 0.5 + 2$ $1 \le 2.5$ This is true, so (1, 1) satisfies the first inequality.

Step2: Test option A: $y > 2x + 1$.

Substitute $x=1$ and $y=1$: $1 > 2(1) + 1$ $1 > 3$ This is false.

Step3: Test option B: $y < 2x - 1$.

Substitute $x=1$ and $y=1$: $1 < 2(1) - 1$ $1 < 1$ This is false.

Step4: Test option C: $y \ge 2x + 1$.

Substitute $x=1$ and $y=1$: $1 \ge 2(1) + 1$ $1 \ge 3$ This is false.

Step5: Test option D: $y \le 2x - 1$.

Substitute $x=1$ and $y=1$: $1 \le 2(1) - 1$ $1 \le 1$ This is true. The point (1, 1) satisfies this inequality.