Questions: y >= -2 * 0 - 3 0 >= -3 y < (-2/3) x - 1 y >= 4 x + 2

Solution Steps

The line passes through the points (0, -1) and (3, -3).

The slope of the line is given by the formula:

\(m = \frac{y_2 - y_1}{x_2 - x_1}\)

Using the points (0, -1) and (3, -3), we have:

\(m = \frac{-3 - (-1)}{3 - 0} = \frac{-2}{3}\)

We can use the point-slope form of a linear equation:

\(y - y_1 = m(x - x_1)\)

Using the point (0, -1) and the slope \(m = -\frac{2}{3}\), we have:

\(y - (-1) = -\frac{2}{3}(x - 0)\) \(y + 1 = -\frac{2}{3}x\) \(y = -\frac{2}{3}x - 1\)

Since the shaded region is above the line and the line is dashed, the inequality is \(y > -\frac{2}{3}x - 1\).

The second line passes through the points (-1, -2) and (0, 2).

The slope of the second line is given by the formula:

\(m = \frac{y_2 - y_1}{x_2 - x_1}\)

Using the points (-1, -2) and (0, 2), we have:

\(m = \frac{2 - (-2)}{0 - (-1)} = \frac{4}{1} = 4\)

We can use the point-slope form of a linear equation:

\(y - y_1 = m(x - x_1)\)

Using the point (0, 2) and the slope \(m = 4\), we have:

\(y - 2 = 4(x - 0)\) \(y - 2 = 4x\) \(y = 4x + 2\)

Since the shaded region is below the line and the line is solid, the inequality is \(y \leq 4x + 2\).

Final Answer