Linear inequalities in two variables

Question

Graph the inequality

x-y<3

Answer 1

Solve for y first as if it were an equal sign

x-y<3

Think : x-y=3 [add y to both sides and subtract 3 on both sides]

x - 3 = y

Slope is 1 and y- intercept is (0, -3)

Graph the point (0,-3) then use the slope to find point before and after that point. If our slope is 1, then go up one and over one to plot point after (0,-3) and go down one and left one for the point before (0,-3). Connect your points lightly then check original problem.

Change back to inequality: x - 3 < y.

This means you will want a dashed line instead of a solid line so you may erase parts of your line at this time. If asked to shade, test out points on both sides of the dashed line. The point that is true, you will shade on the side.

If you test out the origin (0,0) : -3 < 0 is a true statement so the side it is located will be shaded. Hope that helps :)

Answer 2

graph the boundary line, as a dotted line

x-y =3

y=x-3

plot the intercept points: (0,-3) nad (3,0), connect them with a dotted line. extend the dotted line in both directions and put an arrow at the ends to indicate the line goes forever in both directions

the line is upward sloping at a 45 degree angle with the x axis

shade in above the line. the shaded area is the graph of the inequality