Question

Sketch the graph of the inequality. $$y-5 x<0$$

Short answer

The graph of the inequality \(y-5x < 0\) is a dashed line represented by the equation \(y = 5x\). The area that satisfies the inequality is shaded on the side of the line opposite to the origin.

Step-by-step solution

Write the equation for the boundary line

The inequality \(y-5x < 0\) can be rewritten as \(y < 5x\). The boundary line for the solution set is \(y = 5x\). We draw this line first.

Test a point

We can now check a point that does not lie on the boundary line in the inequality to determine which side of the line the solution lies on. The origin \((0,0)\) is always an easy point to choose if it's not on the boundary. Substituting \((0,0)\) into the inequality \(y < 5x\) gives \(0 < 0\), which is false. So the solution to the inequality is not on the side of the line containing the origin.

Draw the final graph

Since the inequality is \(y < 5x\), the line will be dashed to indicate that the points on the line aren't part of the solution set. And because the test point (0,0) shows that the solutions do not lie on the side of the line containing the origin, shade the side of the line opposite to the origin.