Question

two-variable inequalities from their graphs
google classroom microsoft teams
find the inequality represented by the graph.

Explanation:

Step1: Find the slope of the line

The line passes through \((0,0)\) and \((2,1)\). The slope \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{1 - 0}{2 - 0}=\frac{1}{2}\).

Step2: Determine the equation of the line

Using the slope - intercept form \(y = mx + b\), with \(m=\frac{1}{2}\) and \(b = 0\) (since it passes through the origin), the equation of the line is \(y=\frac{1}{2}x\).

Step3: Determine the inequality symbol

The line is solid (so the inequality includes equality) and the shaded region is above the line. For a line \(y=mx + b\), if the shaded region is above the line, the inequality is \(y\geq mx + b\). So substituting \(m=\frac{1}{2}\) and \(b = 0\), we get \(y\geq\frac{1}{2}x\).

Answer:

\(y\geq\frac{1}{2}x\)