which linear inequality is represented by the graph?\n$yleq\\frac{1}{2}x + 2$\n$ygeq\\frac{1}{2}x +…

which linear inequality is represented by the graph?\n$yleq\\frac{1}{2}x + 2$\n$ygeq\\frac{1}{2}x + 2$\n$yleq\\frac{1}{3}x + 2$\n$ygeq\\frac{1}{3}x + 2$

which linear inequality is represented by the graph?\n$yleq\\frac{1}{2}x + 2$\n$ygeq\\frac{1}{2}x + 2$\n$yleq\\frac{1}{3}x + 2$\n$ygeq\\frac{1}{3}x + 2$

Answer

Answer:

A. $y\leq\frac{1}{2}x + 2$

Explanation:

Step1: Find the slope and y - intercept

The line passes through points (-4,0) and (0,2). Slope $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{2-0}{0 - (-4)}=\frac{1}{2}$, y - intercept $b = 2$. So the line equation is $y=\frac{1}{2}x+2$.

Step2: Determine the inequality

The line is solid, so it's either $\leq$ or $\geq$. Test the point (0,0). Substitute into $y$ and $\frac{1}{2}x + 2$: $0\leq\frac{1}{2}(0)+2$ is true. So the inequality is $y\leq\frac{1}{2}x + 2$.