Download Linear Inequalities in Two Variables

Linear Inequalities in Two Variables
Is an ordered pair a solution to a linear inequality?

Plug the x value in for the x and the y value in for the y


If it results in a true statement, the ordered pair is a solution.
If it results in a false statement, it is not a solution.
Graphing a linear inequality:

Temporarily replace your inequality sign with an =.

Solve for y so your equation is in the form y = mx + b
CAUTION: If you have to divide by a negative to solve for y,
you must FLIP your inequality arrow!
4x – 2y < 12
-2y < -4x + 12
y > 2x - 6

Prepare to graph the line but WAIT!
> or <
≥ or ≤
Dashed line (no extra ink for an equal sign)
Solid line (extra ink for an equal sign)
> or ≥
< or ≤
Greater than means shade above the line
Less than means shade below the line
Pick an easy test point.

Remember, the shaded area is all the points that make the
inequality true.

(0, 0) is usually a good test point unless it’s on the line.

Substitute the coordinates of the test point into the original
inequality.

True statement, the point should be in the shaded area.

False statement, the point should be in the unshaded area.
Doing these in MyMathLab is fun! After you graph a solid or dashed
line using the line tool, grab your paint bucket and dump it in the
shaded area.