“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
Ch. 2 Notes Page 7P7 2.2: Linear Equations Part 1
“Failure is not falling down, but refusing to get back up.” – Chinese Proverb
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:
33
2 xy
x y (x, y)33
2 xy
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
)(
)(
runx
riseyslope
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)?
“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
2.2: Linear Equations Part 1HW #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
Ch. 2 Notes Page 8P8 2.2: Linear Equations Part 2
“Failure is not falling down, but refusing to get back up.” – Chinese Proverb
Types of Equations
Slope-Intercept Form y=mx+b
Standard Form Ax+By=C
Point-Slope Form y-y1=m(x-x1)
Horizontal Lines & Vertical Linesy=Number x=Number
Parallel and Perpendicular LinesSlopes and Reciprocals
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 through the point (-6, 2). Write it in standard form. 3
1
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