Question

write an inequality to represent the graph below.

Explanation:

Step1: Find the slope of the line

The line passes through points \((0, 1)\) and \((1, 4)\) (we can also use other points, but these are easy to identify). The slope \(m\) is calculated as \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{4 - 1}{1 - 0}= 3\).

Step2: Determine the y - intercept

The line crosses the \(y\)-axis at \((0,1)\), so the \(y\)-intercept \(b = 1\). The equation of the line in slope - intercept form \(y=mx + b\) is \(y = 3x+1\).

Step3: Analyze the inequality sign

The line is dashed, which means the inequality is strict (either \(>\) or \(<\)). The shaded region is above the line, so for a point \((x,y)\) in the shaded region, \(y>3x + 1\).

Answer:

\(y>3x + 1\)