How do you graph the inequality #y>x - 3# on a coordinate plane.?

1 Answer
Aug 19, 2016

Draw the line as usual. Decide which side is wanted and shade it.
Whether the points on the line are included in the solution or not depends on whether the sign is #>, < >= or <=#


An inequality on a coordinate plane consists of a boundary line and an area in which every point is a possible solution.

If the inequality has a #>= or <=# sign the line will be a solid line and its points are included in the solution.

If the inequality just has a #> or <# sign the line will be a broken or dotted line and its points are not included in the solution.

In this case the equation of the boundary line is # y = x-3#

This line has a slope of 1 and a y-intercept = -3.
The x-intercept is +3. It will be a broken/dashed/dotted line.

To determine which side of the line is the wanted and which is the unwanted region, choose a sample point.

#(0,0)# is a good point.

#0 >0-3#
#0> -3# is true, so the chosen point lies in the wanted region.

In this case, the wanted region is shaded.
graph{y>x-3 [-10, 10, -5, 5]}