which linear inequality is represented by the graph?\n$ygeq\frac{1}{3}x - 4$\n$yleq\frac{1}{3}x…

Explanation:

Step1: Find the slope - intercept form of the line

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. The line passes through two points, say $(0,- 4)$ and $(3,-3)$. The slope $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{-3+4}{3 - 0}=\frac{1}{3}$. The y - intercept $b=-4$ since the line crosses the y - axis at $(0,-4)$. So the equation of the line is $y=\frac{1}{3}x - 4$.

Step2: Determine the inequality

The line is solid, so the inequality is either $y\geq\frac{1}{3}x - 4$ or $y\leq\frac{1}{3}x - 4$. We test a point in the shaded region, say $(0,0)$. Substitute $x = 0$ and $y = 0$ into the inequalities. For $y\geq\frac{1}{3}x - 4$, we have $0\geq\frac{1}{3}(0)-4$, which is $0\geq - 4$ (true). For $y\leq\frac{1}{3}x - 4$, we have $0\leq\frac{1}{3}(0)-4$, which is $0\leq - 4$ (false).

Answer:

$y\geq\frac{1}{3}x - 4$