How do you graph the inequality -4x+3y<-6?

Answer 1

First, solve for y.

add 4x to both sides: 3y<-6+4x

Then divide by 3 : y< -2+4/3x.

Now, you are going to draw the line y= -2+4/3x. This is called the boundary line. Your inequality will be the region on one side of the boundary line. Because it is just a less than (and not also equal to), you draw the line y= -2+4/3x as a dashed line (because it is not included in the solution).

So you have a line, but which side is the graph of the inequality? Pick a point on one side. Any point. Plug it into the inequality. Is it a true statement? If so, that's the side! If not, it's the other side.

It's always a good idea to pick two points, one on either side, just to check your work.