Questions: The graph of which inequality is shown? A. x+y ≤ -1 B. x+y ≥ -1 C. x-y ≤ -1 D. x-y ≥ -1

Solution Steps

The line passes through $(0, -1)$ and $(1, 0)$.

The slope is given by $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ Substituting the points, we get $$m = \frac{0 - (-1)}{1 - 0} = \frac{1}{1} = 1$$

Using the point-slope form of a line, we have $$y - y_1 = m(x - x_1)$$ Substituting the point $(1, 0)$ and slope $1$, we get $$y - 0 = 1(x - 1)$$ $$y = x - 1$$

The shaded region is below the line, which suggests a less than or equal to inequality. Also the line is solid, which indicates the line is part of the solution. Therefore, the inequality represented by the graph is $y \le x - 1$, or equivalently, $x - y \ge 1$.

Final Answer: The correct answer is D. x - y ≥ -1.