Transcript Linear Equations Part 1

Ch. 2 Notes Page 7
P7 2.2: Linear Equations Part 1
“Friendship is born at that moment
when one person says to another,
‘What! You too? I thought I was the
only one.’”
-C. S. Lewis
“Failure is not falling down, but refusing to get back up.” – Chinese
Proverb
Linear Functions/Equations
• A function whose graph is a line is a Linear Function
• A linear function can be represented with a Linear Equation
y=2x+4
•A solution is an (x,y) that makes the equation true.
Graphing Linear Equations
y = mx + b
• y is called the dependent variable because the value of y depends on x
• x is called the independent (or control) variable
Example: Using a table,
graph the equation:
2
y  x3
3
x
y
2
x3
3
y
(x, y)
Standard Form
Standard form of a linear equation is Ax + By = C, where A, B,
and C are real numbers and A, B ≠ 0.
You can graph linear equations in standard form by
finding the x- and y- intercepts
Example: Graph x + y = -2
More Practice
The equation 3x + 2y = 120 models the number of passengers who
can sit in a train car. X is the number of adults and y is the number of
children.
What are the x- and y- intercepts?
What do they represent?
What is the domain? Range?
Slope
y (rise)
slope 
x(run)
Example: What is the slope
of the line through the
points (-3, 4) and (8, -1)?
Example: What is the slope
of the line through the
points (-2,-2) and (4,2)?
Slope (cont.)
y (rise)
slope 
x(run)
What does it mean if the slope is zero? Undefined?
2.2: Linear Equations Part 1
HW #4: 2-2 P67 #3, 6, 8, 11-13, 17-19
“Friendship is born at that moment
when one person says to another,
‘What! You too? I thought I was the
only one.’”
-C. S. Lewis
“Failure is not falling down, but refusing to get back up.” – Chinese
Proverb
Ch. 2 Notes Page 8
P8 2.2: Linear Equations Part 2
“Friendship is born at that moment
when one person says to another,
‘What! You too? I thought I was the
only one.’”
-C. S. Lewis
“Failure is not falling down, but refusing to get back up.” – Chinese
Proverb
Types of Equations
Slope-Intercept Form
Standard Form
Point-Slope Form
y=mx+b
Ax+By=C
y-y1=m(x-x1)
Horizontal Lines & Vertical Lines
y=Number
x=Number
Parallel and Perpendicular Lines
Slopes and Reciprocals
Slope-Intercept Form
y = mx + b
m=3 and (2,4)
Standard Form
Ax+By=C
4x+8y=24
Find the x- and y-intercepts
Point-Slope Form
The line through the point (x1, y1) with slope m has the equation
y – y1 = m(x – x1)
Example: Find the equation of a line with slope
point (-6, 2). Write it in standard form.
1 through the

3
Point-Slope Form
The line through the point (x1, y1) with slope m has the equation
y – y1 = m(x – x1)
Example: Find the equation of a line through the points (-2, 3) and
(1, 6). Write it in standard form.
Slope-Intercept Form
y = mx + b
What is the slope of the line
4x + 6y = 18?
What is the slope of:
a horizontal line?
a vertical line?
parallel lines?
perpendicular lines?
Example: Write an
equation through the
point (3, 5) and
perpendicular to the line
7x – 21y = 42
3 equations for a line
Slope-intercept: y = mx + b
slope
y-intercept
Point-slope: y – y1 = m ( x – x1 )
(x,y) point on line
Standard Form: A x + B y = C
numbers
2.2: Linear Equations Part 2
HW #5: 2-2 P68 #20, 24, 26, 30, 32, 36, 43, 45,
“Friendship is born at that moment
48, 51, 57
when one person says to another,
‘What! You too? I thought I was the
only one.’”
-C. S. Lewis
“Failure is not falling down, but refusing to get back up.” – Chinese
Proverb