Objectives: Students will write, solve, and graph linear inequalities with one and two
variables.
Warm-up: (Get a sheet of graph paper from the back of the room.)
Find the x and y intercepts for this inequality:
y + 3x > 4
x-intercept: set y = 0 and solve for x
y-intercept: set x = 0 and solve for y
Find the slope for this line. (y = mx + b, where m = slope and b = y-intercept)
Using a complete sentence, explain how you would draw this line on a graph. (There
are at least three right answers.)
Graphing inequalities.
Step 1: Graph the boundary line.
Solid boundary line: < or >
Dashed boundary line: < or >
Step 2: Plug in a test point that is not on the boundary line.
Step 3: Shade in the answer to the inequality.
Practice:
y ≥ (1/2) x - 1
Step 1: Graph the boundary line.
You can use:
1) Slope intercept: y ≥ (1/2) x - 1
y = mx + b, where m = slope and b = y-intercept
y ≥ (1/2) x - 1, slope = 1/2 and y-intercept = -1
Therefore, plot (0, -1) and then draw a line with slope =
1/2
or
2) Find x and y intercepts.
How?
Set y = 0 and solve for x: y ≥ (1/2) x - 1
0 = (1/2)x - 1
1 = (1/2)x
2=x
Therefore, (2, 0)
and
Set x = 0 and solve for y: y ≥ (1/2) x - 1
y = (1/2)(0) - 1,
y = -1
Therefore, (0, 1)
Solid boundary line: < or >
Dashed boundary line: < or >
Step 2: Plug in a test point that is not on the boundary line.
Any number will do, but (0,0) usually works.
y ≥ (1/2) x - 1
0 ?≥? (1/2) (0) - 1
0 ?≥? - 1 --> Yes!
Step 3: Shade in the answer to the inequality.
Which side of the line is (0,0) on?
Practice:
y ≤ 2x - 5
Step 1: Graph the boundary line.
Step 2: Plug in a test point that is not on the boundary line.
Step 3: Shade in the answer to the inequality.
Inequality Quiz.
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30 minutes
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