Graphing Inequalities
Graphing Inequalities
Examples of Graphing Inequalities
Example Work Out Problem
6.3 Graphing Inequalities
Graphing Linear Inequalities
Review!
Before we can start, we might benefit from a little review of graphing a linear equation.
Graphing a Line (Review)
Step 1: Start with the y intercept plot point on the coordinate plane
Graphing Inequalities
Your Turn! Let's Practice!
Practice
Change the following from
STANDARD
to
SLOPE INTERCEPT
FORM.
Standard 
Ax + By = C
(i.e. 10x + 5y = 20)
SlopeIntercept
y = mx + b
(i.e. y = 3x + 8)
What
: Graphing linear inequalities on a coordinate plane
How
: 1. Graph the equation of the line
2. Shade in the area of the solution on the graph
Line types:
slopeintercept form:
y = mx + b
standard form:
Ax + By = C
SlopeIntercept Form
y = mx + b
Remember: x = input and y = output
m = slope
b = y intercept
slope =
rise
run
change in y
change in x
=
y intercept = where the line crosses the y axis
How to graph an inequality in slope intercept form
Step 2: From the y intercept, use the slope to graph the line.
y = 4x  2
Example:
1. What is the y intercept?
2. What is the slope?
Graphing Equations
Graphing Inequalities
All lines are solid lines
Greater than/ Less than = dashed line
Greater/Less than or equal to = solid line
Just the line with no shading
Greater than shade area above the line
Less than shade area under the line
and
solid
line when graphing
y < or y
shade
under
the line
y > or y
shade
over
the line
<
and
>
dotted
line when graphing
y < x + 1
1. greater than or equal
to symbol = solid line
2. 5 = y intercept;
slope = 2 (rise) / 1 (run)
3. Since y is GREATER
than or equal to, shade
ABOVE the line
1. Less than sign dotted line
2. Y intercept = 1;
slope = 1(rise)/ 1(run)
3. Y is LESS THAN = shade under
the line
Problem:
y
3x + 5
1. Locate y intercept = 5
2. Use slope 3 (rise) / 1 (run)
3. Graph 34 points on graph
4. Graph a solid line [or equal to]
5. Shade in below the line (less than)
STEPS FOR SOLVING:
1. Plot y intercept
2. Locate slope Rise/Run
3. Graph 34 points using slope
4. Graph a solid/dotted line
depending on greater than/less than
or greater/less than or equal to
5. Shade above or below line
depending on greater than or less than
Answer: y 3x + 5
Check your work!
Did you get it right? :)
Standard Form vs. SlopeIntercept Form
1.
2.
3.
1.
2.
3.
Challenge
: When you're given an inequality in
STANDARD FORM
Ax + By < C
, change it to
SLOPEINTERCEPT FORM
y < mx + b
before you graph!
!
Example:
10x + 5y < 40
I want the Y by itself on one side, so first, subtract 10x on both sides.
10x
10x
5y < 40  10x
Divide by 5 on each side
5
5
y <
40
5

10x
5
< 8  2x
Switch the order to make it to be slopeintercept form
y < 2x + 8
9x  3y < 18
*Change into slopeintercept form, then graph!
*Remember, if you multiply or divide by a negative number, flip the sign!
Answer
9x  3y < 18
9x
9x
3y < 18  9x
3
3
y
>
6 + 3x
y
>
3x  6
graph of
y > 3x  6
* dashed line y is greater than (not equal to)
*greater than shade OVER the line
Graph should look something like this
y = 4x  2
PLOT AT LEAST 3 POINTS BEFORE GRAPHING LINE!
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6.3 Graphing Linear Inequalities
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