AA Section 3-4
40
Section 3-4 The Graph of Ax + By = C
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The Graph of Ax + By = C
Transcript of AA Section 3-4
Section 3-4T h e G r a p h o f A x + B y = C
Warm-upGraph the following.
1. y = 3x + 6 2. y = 2
3x − 4
Warm-upGraph the following.
1. y = 3x + 6 2. y = 2
3x − 4
Warm-upGraph the following.
1. y = 3x + 6 2. y = 2
3x − 4
Warm-upGraph the following.
1. y = 3x + 6 2. y = 2
3x − 4
Question: What do you notice about these two graphs?
Standard Form of an Equation for a Line:
Standard Form of an Equation for a Line: Standard form; Ax + By = C, where A, B ≠ 0
Standard Form of an Equation for a Line: Standard form; Ax + By = C, where A, B ≠ 0
“Shocking” Theorem:
Standard Form of an Equation for a Line: Standard form; Ax + By = C, where A, B ≠ 0
“Shocking” Theorem: The graph of Ax + By = C,
Standard Form of an Equation for a Line: Standard form; Ax + By = C, where A, B ≠ 0
“Shocking” Theorem: The graph of Ax + By = C, where A, B ≠ 0,
Standard Form of an Equation for a Line: Standard form; Ax + By = C, where A, B ≠ 0
“Shocking” Theorem: The graph of Ax + By = C, where A, B ≠ 0,is a line!
Standard Form of an Equation for a Line: Standard form; Ax + By = C, where A, B ≠ 0
“Shocking” Theorem: The graph of Ax + By = C, where A, B ≠ 0,is a line!
Proof:
Standard Form of an Equation for a Line: Standard form; Ax + By = C, where A, B ≠ 0
“Shocking” Theorem: The graph of Ax + By = C, where A, B ≠ 0,is a line!
Proof: Ax + By = C
Standard Form of an Equation for a Line: Standard form; Ax + By = C, where A, B ≠ 0
“Shocking” Theorem: The graph of Ax + By = C, where A, B ≠ 0,is a line!
Proof: Ax + By = C-Ax -Ax
Standard Form of an Equation for a Line: Standard form; Ax + By = C, where A, B ≠ 0
“Shocking” Theorem: The graph of Ax + By = C, where A, B ≠ 0,is a line!
Proof: Ax + By = C-Ax -AxBy = -Ax + C
Standard Form of an Equation for a Line: Standard form; Ax + By = C, where A, B ≠ 0
“Shocking” Theorem: The graph of Ax + By = C, where A, B ≠ 0,is a line!
Proof: Ax + By = C-Ax -AxBy = -Ax + CB B
Standard Form of an Equation for a Line: Standard form; Ax + By = C, where A, B ≠ 0
“Shocking” Theorem: The graph of Ax + By = C, where A, B ≠ 0,is a line!
Proof: Ax + By = C-Ax -AxBy = -Ax + CB B
y = −
AB
x +CB
Standard Form of an Equation for a Line: Standard form; Ax + By = C, where A, B ≠ 0
“Shocking” Theorem: The graph of Ax + By = C, where A, B ≠ 0,is a line!
Proof: Ax + By = C-Ax -AxBy = -Ax + CB B
y = −
AB
x +CB
m = −
AB
Standard Form of an Equation for a Line: Standard form; Ax + By = C, where A, B ≠ 0
“Shocking” Theorem: The graph of Ax + By = C, where A, B ≠ 0,is a line!
Proof: Ax + By = C-Ax -AxBy = -Ax + CB B
y = −
AB
x +CB
m = −
AB
b =CB
Example 1State the slope and y-intercept without rewriting the equation
4x + 7y = 21.
Example 1State the slope and y-intercept without rewriting the equation
4x + 7y = 21.
m =
Example 1State the slope and y-intercept without rewriting the equation
4x + 7y = 21.
m = −
AB
Example 1State the slope and y-intercept without rewriting the equation
4x + 7y = 21.
m = −
AB
= −47
Example 1State the slope and y-intercept without rewriting the equation
4x + 7y = 21.
m = −
AB
= −47
b =
Example 1State the slope and y-intercept without rewriting the equation
4x + 7y = 21.
m = −
AB
= −47
b =
CB
Example 1State the slope and y-intercept without rewriting the equation
4x + 7y = 21.
m = −
AB
= −47
b =
CB
=217
Example 1State the slope and y-intercept without rewriting the equation
4x + 7y = 21.
m = −
AB
= −47
b =
CB
=217
= 3
Example 1State the slope and y-intercept without rewriting the equation
4x + 7y = 21.
m = −
AB
= −47
b =
CB
=217
= 3
y-int = (0, 3)
Some things to be aware of
Some things to be aware of
*Slope-Intercept:
Some things to be aware of
*Slope-Intercept: We can represent oblique and horizontal lines, but not vertical
Some things to be aware of
*Slope-Intercept: We can represent oblique and horizontal lines, but not vertical
*Standard Form:
Some things to be aware of
*Slope-Intercept: We can represent oblique and horizontal lines, but not vertical
*Standard Form: We can represent all types of lines
Some things to be aware of
*Slope-Intercept: We can represent oblique and horizontal lines, but not vertical
*Standard Form: We can represent all types of lines
Another benefit of standard form:
Some things to be aware of
*Slope-Intercept: We can represent oblique and horizontal lines, but not vertical
*Standard Form: We can represent all types of lines
Another benefit of standard form: We can graph by intercepts
Example 2Graph 10x + 6y = 30
Example 2Graph 10x + 6y = 30
x y
0 5
3 0
Example 2Graph 10x + 6y = 30
x y
0 5
3 0
Homework
Homework
p. 160 #1-26
“The future belongs to those who prepare for it today.” - Malcolm X
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