Example 1

Graph the solutions to the inequality $y>3x-2$.

First, graph the line $y=3x-2$, but draw it dashed since $>$ means the boundary line is not part of the solution. For example, the point $\left(0,-2\right)$ is on the boundary line, but it is not a solution to the inequality because $-2\cancel>3\left(0\right)-2$ or $-2\cancel>-2$.

Next, test a point that is not on the boundary line. 
For this example, use the point $\left(-2,4\right)$.

$4>3\left(-2\right)-2, \text{ so } 4>-8$ which is a true statement. 

Since the inequality is true for this test point, shade the region containing the point $\left(-2,4\right)$. All of the coordinate pairs that are solutions lie in the shaded region.