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

Jun 17, 2016

It is easier to work with straight lines in the form $y = m x + c$

In this case: $y < - x + 3$

One can choose x-values, work out y-values and plot points, or, use the slope and intercept method.

This line crosses the y-axis at 3 and has a gradient of -1.
(ie it is at 45° from top left to bottom right, cutting the y-axis at 3).

However, as this is an inequality with only a "less than" sign, the line should be drawn as a dotted line, meaning that points on the line are not part of the solution.

The solution is shown by shading the wanted area which is the part of the plane lying below the drawn line.