Question

linear inequalities: mastery test

Explanation:

Identify the boundary line

The boundary line is dashed and passes through the y-intercept \((0, -1)\) and the x-intercept \((-3, 0)\).
Using the intercept form or slope-intercept form:

$$ \text{Slope } m = \frac{-1 - 0}{0 - (-3)} = -\frac{1}{3} $$

$$ \text{Equation of the line: } y = -\frac{1}{3}x - 1 $$

Determine the inequality sign

The region above the dashed line is shaded.
Since the line is dashed, the inequality is strict (\(>\)).

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

Convert to standard form

Multiply the entire inequality by 3 to clear the fraction:

$$ 3y > -x - 3 $$

$$ x + 3y > -3 $$

Answer:

$$x + 3y > -3$$