2. What is a Linear Inequality?
• An inequality containing x and y
whose boundary is a straight line.
3. Checking Solutions
• Solutions of linear inequalities are
ordered pairs (x, y) that make the
inequality true.
• To check if a point is a solution:
▫ Plug it in for x and y
▫ Simplify
▫ Does it make a true statement?
9. Graphs of Linear
Inequalities
• Linear inequalities, like linear
equations, cannot be “solved” to get a
number answer.
• Instead, we use a graph to show all
solutions!
• Graphs will contain a “boundary
line” and a shaded “half plane.”
10. Dashed or Solid
• A dashed line means points on
the line are not solutions.
▫ Use for < and >.
• A solid line means points on the
line are solutions.
▫ Use for ≤ and ≥.
11. Where to Shade?
• The shaded area shows all possible
points that make the inequality true.
• Test a point.
▫ We usually use (0,0).
▫ If it is on the line, choose a different
point.
• If it is a solution, shade that side.
• If it is not a solution, shade the other
side.
12. Graphing Simple Linear
Inequalities
• Linear inequalities with only one
variable have horizontal or vertical
boundary lines.
• x: vertical (up and down)
• y: horizontal (side to side)