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

Explanation:

Step1: Identify 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 $b=-2$. So the statement "The slope of the line is - 2" is false.

Step2: Determine line type

When the inequality is $y>mx + b$ (strict inequality), 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 shading 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 statement "One solution to the inequality is $(0,0)$" is true.

Step5: Find y - intercept

The y - intercept of the line $y=\frac{3}{4}x - 2$ is the value of $y$ when $x = 0$. Substituting $x = 0$ gives $y=-2$. 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 $(0,-2)$