which linear inequality is represented by the graph?\no $y\\leq\\frac{1}{3}x - 1$\no $y\\geq\\frac{1}{3}x…

Explanation:

Step1: Find the slope and y - intercept of the line

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

Step2: Determine the inequality sign

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

Answer:

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