When you are asked to graph an inequality, you would expect a graph with a shaded region. This is because the curve or line does not actually have those data points as the solution. It is the data points above or below the curve or line.
First, you disregard the inequality to graph the equation. Find the x- and y-intercepts, plot them, and connect these two dots by extending infinitely from both sides.
x-intercept: let y = 0
0 - 2x = -18
x = 9
y-intercept: let x = 0
3y- 0 = -18
y = -6.
The graph is shown in the picture. Next, you test the inequality by choosing a random data point that does not coincide with any of the data points passed by the line. Suppose, we choose the origin (0,0)
3y- 2x > -18
3(0) - 2(0) > -18
0 > 18
The inequality is true for (0,0), Thus, the shaded region must include this point. All of the region to the left bounded by the line is a solution. Note that the data points are hollow because they are not part of the solution because of the inequality '>'. If it were ≥, then those points would be solid.
