how do you graph 3x - 5y < 15

Answer 1

First, graph the related equation (3x - 5y =15)

Since the equation is in standard form, the simplest way to do this is by finding the intercepts. Set x=0 and solve for y gives you the y-intercept (0,-3). Set y=0 and solve for x gives you the x-intercept (5,0).

Plot the two points on the coordinate plane, then draw a broken line through them. (The broken line is used for < and > inequalities to signify that the point ON the line are NOT part of the solution set. If you have a ≤ or ≥ inequality, the line is solid, signifying that points on the line ARE part of the solution set.

Once you have graphed the equation, you must decide on which side of the graph contains the solutions to the inequality. You can pick any point on either side of the graph (not a point on the graph) and plug the coordinates into the inequality to see if true. I chose (0,0) which lies above the graph. 3(0) - 5(0) < 15? Since zero is not less than 15 the statement is false. Therefore all points on the other side of the graph (below it) contain all solutions to the inequality, so we shade in below the broken line.