SM-1
Name:_________________________
021014
Date:____________ Hour:________
6.5: Linear Inequalities
CCS –Algebra »Reasoning with Equations and Inequalities: D.12
Learning Goal:
I will determine whether an ordered pair is a solution to a linear inequality.
I will graph linear inequalities.
Essential Understanding. Linear inequalities have an infinite number of solutions that can be
represented in a graph by all the points on one side of a boundary line.
Vocabulary
Linear inequality: are formed when we replace an equal sign in a linear equation with an
inequality symbol instead.
Solution of an inequality: an ordered pair (or point) that makes the inequality true.
Identifying Solutions of a LinearInequality:
EX 1: Determine whether each ordered pair is a solution to𝑦 > 𝑥 − 3.
a) (-3, -7)
Substitute the x and y
values of the point in
for the given inequality,
then simplify.
b) (1, 2)
The graph of a linear inequality consists of all points that represent solutions.
We start by drawing a boundary line, then shading the area where the solutions lie.
The boundary line is dashed if the inequality has the symbols:
Points on the dashed line are NOT solutions.
The boundary line is solid if the inequality has the symbols:
Points on the solid line are solutions.
Graphing Inequalities:
EX 2: Graph 2𝑦 > 3𝑥 − 2.
Step 1: Make sure the inequality is solved for y.
Step 2: Graph the border line as solid or dashed.
Slope:
y-int:
solid or dashed?
Step 3: Test a point not on the border line to determine where to shade.
Test point: ( ___, ___ )
Plug point in.
 If the inequality is true, then the point is part of the solution area and we
shade that side of the border line.
 If the inequality is false, then the point is NOT part of the solution area and
we shade the other side of the border line.
EX 3: Graph 𝑥 ≤ −3.
Step 1: Make sure the inequality is solve for y.
Step 2: Graph the border line as solid or dashed.
Slope:
y-int:
solid or dashed?
Step 3: Test a point not on the border line to determine where to shade.
Test point: ( ___, ___ )
Plug point in.
EX 4: Graph 𝑦 − 2𝑥 ≥ −5.
Step 1: Make sure the inequality is solve for y.
Step 2: Graph the border line as solid or dashed.
Slope:
y-int:
solid or dashed?
Step 3: Test a point not on the border line to determine where to shade.
Test point: ( ___, ___ )
Plug point in.
EX 5: Graph 𝑦 < 2.
Step 1: Make sure the inequality is solve for y.
Step 2: Graph the border line as solid or dashed.
Slope:
y-int:
solid or dashed?
Step 3: Test a point not on the border line to determine where to shade.
Test point: ( ___, ___ )
Plug point in.
Using Inequalities to Model Real Life Situations:
EX 6: Cedric is going to remodel a kitchen. He’s going to use wallpaper for the 24 foot
area between the counters & the cabinets, and tile for the 12 foot area above the stove.
His budget is at most $420. Write a linear inequality to represent this situation, graph
it, and find 3possible prices for the wallpaper and tile he could buy.
Variables: Let x = cost per square ft of wallpaper
Let y = cost per square ft of tile
Inequality:_________________________
Solve for y:
Graph:
Three possible prices:
EX 7: Haden is buying paperback and hardcover books at a book sale. He only has a $20
bill on him. Paperbacks are $2.50 and hardcovers are $4.50. Write a linear inequality
to represent this situation, graph it, and find 3possible combinations of paperback and
hardcover books he could buy.
Variables: Let x = number of hardcover books
Let y = number of paperback books
Inequality:_________________________
Solve for y:
Graph:
Three possible combinations:
Writing Inequalities from Graphs:
EX 8: Write a linear inequality that represents this graph.
Step 1: Identify the slope and y-intercept as we read the graph from left to right.
Slope:
y-int:
Step 2: Put in slope intercept form. y
___x + ____
Step 3: Determine if the inequality will be < , > 𝑜𝑟 ≤ , ≥
Step 4: If the shaded are is below the border line it will be < 𝑜𝑟 ≤.
If the shaded region is above the border line it will be > 𝑜𝑟 ≥.
Step 5: Write the inequality.
EX 9: Write a linear inequality that represents this graph.
Step 1: Identify the slope and y-intercept as we read the graph from left to right.
Slope:
y-int:
Step 2: Put in slope intercept form.
y
___x + ____
Step 3: Determine if the inequality will be < , > 𝑜𝑟 ≤ , ≥
Step 4: If the shaded are is below the border line it
will be < 𝑜𝑟 ≤.If the shaded region is above the border line it will be > 𝑜𝑟 ≥.
Step 5: Write the inequality.
EX 10: Write a linear inequality that represents this graph.
Step 1: Identify the slope and y-intercept as we read the graph from left to right.
Slope:
y-int:
Step 2: Put in slope intercept form. y
___x + ____
Step 3: Determine if the inequality will be < , > 𝑜𝑟 ≤ , ≥
Step 4: If the shaded are is below the border line it will
be < 𝑜𝑟 ≤. If the shaded region is above the
border line it will be > 𝑜𝑟 ≥.
Step 5: Write the inequality.