Graphing the Solution to Multiple Inequalities

In an earlier chapter we learned how to graph an inequality on a number line. Now we look at graphing inequalties on the coordinate plane.

To graph an inequalitiy we will use the same procedure as graphing an equation.

Simplify the inequality first then use the slope and intercept to graph.

2y > 4x - 6


2y > 4x - 6
2

y > 2x - 3

We anchor our line with the y-intercept and use the slope to extend the line in both directions.

With inequalities we use two different forms of a line:

dash or broken line for greater than or less than
or
solid line for great than or equal to or less than or equal to

But with inequalities we also shade in the section of the coordinate plane that includes all the possible values for y

If y is greater than 2x - 3 we shade in above the line.

For y is less than -x + 4 we shade below the line.

When we graph two inequalities we shade each individually and the area where they overlap is the solution to both inequalities

Important steps: simplify the inequality, graph the line using y-intercept and slope with either a dashed or solid line, shade above for greater and below for less.

Graphing Inequalities on a Number Line

When graphing inequalities on a number line there are conventions for the direction of the line and the end point of the line.

The end point is closed (filled in) when the symbols are

≤ less than or equal to
or
≥ greater than or equal

The end point is open when the symbols are

< less than
or
> greater than

The direction of the line on the graph is determined by whether the amount is greater than (going to the right on the number line) or less than (going to the left on the number line).

If the inequality is written with the variable on the left then the inequality symbol points in the direction of the line.