### Name Date ______ Unit 3 – Graphing Math 8 Aim #40: How do we

```Name _____________________________
Unit 3 – Graphing
11-28-16
Date ____________
Math 8
Aim #40: How do we graph linear inequalities in two variables?
HW #40: Graphing Linear Inequalities Handout
Do Now: Write the equation of the line passing through the points (9, -3) and (5, -11).
Graphing Linear Inequalities
Example: a) Graph the equation y = 3x + 5.
b) Does changing the equation y = 3x + 5
to the inequality y ≥ 3x + 5 change the
solution set of the graph? Show examples
c) Now represent y ≥ 3x + 5 on the graph below.
d) How would the graph from part c be different if we change y ≥ 3x + 5 to
y > 3x + 5? Represent y > 3x + 5 on the graph.
1) a) Graph y - 2x ≤ 3.
Step 1: Solve the inequality for
____ first!
Step 2: Graph the inequality just like
you graph a linear equation by
identifying the ________ and
___________.
Step 3: Connect the points to form
the __________ line.
Step 4: Choose a ______ point to
determine which side of the boundary
line to shade for the solution set.
Step 5: Label the graph with the
__________ inequality.
a) Is (5, 1) a solution to the inequality?
b) Is (-7, 4) a solution to the inequality?
The solution of an inequality are the coordinates on the region of a graph
that make the inequality true.
1) Boundary Line:
a) ≤ or ≥
b) < or >
solid line
dashed line
2) Shading: Substitute a test point into the original inequality.
If the inequality is true, shade the region with the test point
If the inequality is false, shade the region without the test point
What would be the easiest test point to use?
When can you not use your answer from the previous question as a test
point?
Graph each inequality.
2) 3x - 5y < 10
3) x + 3y ≤ -6
4) x < 2
5) y ≥ -5
6) y - 5 < 3(x + 1)
Circle the ordered pairs that are solutions to the inequality 4x - y ≤ 10.
(2, 3)
(6, 0)
(4, -1)
(1, -6)
(-2, -18)
Summmary: We use a ___________ line when graphing the inequalities < or >.
We use a ___________ line when graphing the inequalities ≤ or ≥.
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