which statements are true about the linear inequality y > 3/4x - 2? select three options. the slope of the…

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 $b=-2$.

Step2: Analyze line type

Since the inequality is $y>\frac{3}{4}x - 2$ (a strict inequality), the graph of the line $y = \frac{3}{4}x-2$ is a dashed line.

Step3: Determine shading region

For $y>\frac{3}{4}x - 2$, the area above the line is shaded.

Step4: Check if a point is a solution

Substitute $(x = 0,y = 0)$ into the inequality: $0>\frac{3}{4}(0)-2$, which simplifies to $0>-2$. So, $(0,0)$ is a solution.

Step5: Find y - intercept

The y - intercept of the line $y=\frac{3}{4}x - 2$ is the point where $x = 0$. When $x = 0$, $y=-2$, so the graph intercepts the y - axis at $(0,-2)$.

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 $(0,-2)$.