which inequality is graphed on the coordinate plane?\na. $y < 4x + 2$\nb. $y > 4x + 2$\nc. $yleq\frac{1}{4}x…

Explanation:

Step1: Identify the slope - intercept form

The general form of a linear inequality is $y>mx + b$ or $y<mx + b$ or $y\geq mx + b$ or $y\leq mx + b$, where $m$ is the slope and $b$ is the y - intercept.

Step2: Find the y - intercept

The line intersects the y - axis at $y = 2$, so $b = 2$.

Step3: Find the slope

Using two points on the line, say $(0,2)$ and $(- 0.5,0)$. The slope $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{0 - 2}{-0.5-0}=4$.

Step4: Determine the inequality type

The line is solid, so the inequality is either $y\geq mx + b$ or $y\leq mx + b$. Also, the shaded region is below the line, so the inequality is $y\leq mx + b$.

Answer:

E. $y\leq4x + 2$