Question

this is the graph of a linear inequality. write the inequality in slope - intercept form.

Explanation:

Step1: Find the slope of the line

The line passes through \((0, 3)\) and \((-4, 0)\). The slope \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{0 - 3}{-4 - 0}=\frac{-3}{-4}=\frac{3}{4}\).

Step2: Determine the y - intercept

The line crosses the y - axis at \((0, 3)\), so the y - intercept \(b = 3\). The equation of the line in slope - intercept form is \(y=mx + b\), so the equation of the boundary line is \(y=\frac{3}{4}x+3\).

Step3: Determine the inequality symbol

The line is dashed, so the inequality is either \(y>\frac{3}{4}x + 3\) or \(y<\frac{3}{4}x+3\). We test a point in the shaded region, for example, \((0,4)\). Substitute \(x = 0\) and \(y = 4\) into the inequality \(y\) \(\_\_\) \(\frac{3}{4}x+3\). When \(x = 0\), \(\frac{3}{4}(0)+3=3\). Since \(4>3\), the inequality is \(y>\frac{3}{4}x + 3\).

Answer:

\(y>\frac{3}{4}x + 3\)