2.5-1: Linear Inequalities
• Similar to linear equations, we can graph the
solutions to linear inequalities
• Differences?
– Equation = solutions lying on a line
– Inequalities = solutions lying in solution “sets” and
possibly the line as well
• We will still graph the same way as before
– Slope-Intercept
– Point-Slope
– X and Y intercepts
• However, with inequalities, we must shade,
and use a specific line
Shading, Types of Lines
• <, > = Dotted Line
• ≥, ≤ = Solid Line
• <, ≤ = Shade Below OR Left
• >, ≥ = Shade Above OR Right
• Example. Graph the linear inequality
3x – 4y < 12
– Solid, Dotted?
– Where can we shade?
• Example. Graph the inequality -2y ≤ -x + 4
AND/OR Combinations
• Recall…
– AND = contains elements two sets share
– OR = contains all elements of both sets
• When graphing two inequalities, we can use
the same rules
• AND = look where shading overlaps
• OR = include all shaded areas
• Example. Graph the solution set to the
inequalities 5x – 2y < 10 AND y ≤ x.
– Use same plot; 2 colors helps
• Example. Graph the solution set to the
inequalities x ≥ 1 OR y > 2.
– Include both areas
• Assignment
• Pg. 170
• 1-27 odd