Question

what inequality is shown in the graph?

Explanation:

Find the boundary line equation

The boundary line is dashed, passing through the y-intercept \((0, 1)\) and the x-intercept \((-0.33, 0)\), or more clearly through points \((0, 1)\) and \((-1, -2)\).

$$ \text{Slope } m = \frac{-2 - 1}{-1 - 0} = \frac{-3}{-1} = 3 $$

$$ \text{Equation: } y = 3x + 1 $$

Determine the inequality sign

The boundary line is dashed, so the inequality is strict (\(<\) or \(>\)).
The shaded region is to the left/above the line. Testing the point \((-2, 0)\):

$$ 0 > 3(-2) + 1 \implies 0 > -5 \quad (\text{True}) $$

Thus, the inequality is:

$$ y > 3x + 1 $$

Answer:

What inequality is shown in the graph? <blank>\(y > 3x + 1\)</blank>