Questions: Which inequality is graphed on the coordinate plane? A. y<-2 x=1 B. y>-2 x-1 C. y ≤-2 x-1 D. y ≥-2 x-1

Solution Steps

The line passes through the points $(0, -1)$ and $(-1, 1)$. The slope of the line is $m = \frac{1 - (-1)}{-1 - 0} = \frac{2}{-1} = -2$. The y-intercept is $-1$. So, the equation of the line is $y = -2x - 1$.

The shaded region is below the line, which means the inequality is either $y < -2x - 1$ or $y \leq -2x - 1$. The line is solid, which means the inequality includes the line. So the inequality sign is $\leq$.

The inequality is $y \leq -2x - 1$.

Final Answer