Linear Inequalities and Their Graphs
Graphing linear inequalities is similar to graphing linear equations. The same rules apply for determining the slope and y‐intercept.
However, the graphs look slightly different because the lines can either be dashed or solid and include shading depending on the sign of the inequality.
The rules for graphing linear inequalities are:
Because the ISEE is a multiple test, you will not need to graph linear inequalities by hand. However, you will need to know what the graph of a linear inequality will look like by recognizing patterns from linear equations. Linear inequalities with positive slopes will point upwards and those with negative slopes wil point downwards.
If you receive an inequality with y and x, but the equation is not in slope-intercept form (y = mx + b), rearrange the equation so "y" is on the left and everything else on the right.
For example: 3x + y = 9 can be rearranged as y = -3x + 9
When deciding between two answer choices that look very similar, plug in values for x or y and match the corresponding points to the correct graph. Try the question below for practice:
Which inequality matches the graph below?
- A) y < x2 + 1
- B) y > x2 + 1
- C) y ≤ x2 + 2
- D) y > x2 + 2
We can eliminate C because we need a solid line for the ≤ sign. We can also eliminate choice A because we shade below the line for the < symbol. Now, we are left between answer choices B and D.
Notice that +1 is the y-intercept of this graph, which would correspond to choice B. If you would still like to verify this answer plug in x and y values for choices B and D:
The points for choice B matches the graph, so B is the correct answer.
Practice Problems
Answers to Practice Problems
- A
- A
- D
- B
- A
- B
