which statements are true about the linear inequality y > \\frac{3}{4}x - 2? select three options.\nthe…

Explanation:

Step1: Recall slope - intercept form

The linear inequality is in the form $y>mx + b$, where $m$ is the slope and $b$ is the y - intercept. For $y>\frac{3}{4}x - 2$, the slope $m=\frac{3}{4}$ and the y - intercept is at $(0,-2)$. So the statement "The slope of the line is - 2" is false.

Step2: Analyze the type of line

For a strict inequality like $y>mx + b$ (no equal - to sign), the graph of the boundary line $y = mx + b$ is a dashed line. So the statement "The graph of $y>\frac{3}{4}x - 2$ is a dashed line" is true.

Step3: Determine the shaded region

For $y>mx + b$, the area above the line $y=mx + b$ is shaded. So the statement "The area below the line is shaded" is false.

Step4: Check a point

Substitute $x = 0$ and $y = 0$ into the inequality $y>\frac{3}{4}x - 2$. We get $0>\frac{3}{4}(0)-2$, which simplifies to $0>-2$. So the point $(0,0)$ is a solution to the inequality, and the statement "One solution to the inequality is $(0,0)$" is true.

Step5: Find the y - intercept

In the equation $y=\frac{3}{4}x - 2$, when $x = 0$, $y=-2$. So the graph intercepts the y - axis at $(0,-2)$, and the statement "The graph intercepts the y - axis at $(0,-2)$" is true.

Answer:

The graph of $y>\frac{3}{4}x - 2$ is a dashed line; One solution to the inequality is $(0,0)$; The graph intercepts the y - axis at $(0,-2)$.