Replace the inequality in the slope intercept form with an equal sign. The graph of this equation will delineate the boundary of the graph of the inequality. The graphs of inequalities define regions and the graph of this related equation shows the boundary of the region.
List two points in the slope intercept form equation. Slope intercept forms all look like this: Y = mX + b where m is the slope of the line and b is the point where the line crosses the Y axis. You can find one of the points by leting X = 0 and solving for Y, and you can find another point by letting Y = 0 and solving for X. As the graph is a line, these two poinrs will allow you to draw the line. For example, if you are graphing Y = 3X - 2, one of the points will be (0, -2) and the other will be (3/2, 0). Connect these two points and extend the line segment to the edges of the graph.
Determine which side of the line represents the region of the graph. You can do this by picking a point that is not on the line and testing to see if this point in in the region. If the line does not go through the origin (0, 0), this is a good point to choose because it makes the arithmetic easy. For example, if the inequality is Y is-less-than 3X - 2, the associated equation is Y = 3X - 2 and the graphed line does not go through the origin. If we substitute the point (0, 0) in Y is-less-than 3X - 2 we get 0 is-less-than 3(0) - 2 or 0 is-less-than -2. This is false, so the origin is not part of the region of the graph. The region is on the other side of the line Y = 3X -2.