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6.3 Graphing Linear Inequalities
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Transcript of 6.3 Graphing Linear Inequalities
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!
Full transcriptGraphing 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!