Title: Rates of Change (Slope)
1Rates of Change (Slope)
2After this lesson, you should be able to
- find the slope of a line passing through two
points - write the equation of a line given the point and
the slope - sketch the graph of a linear equation in
slope-intercept form - write equations of lines that are parallel or
perpendicular to a given line
3Slope of a Line
Slope
Also,
A line has the same slope everywhere.
4Equations of Lines
To write the equation of a line, you need
Remember Equations of lines are first degree
equations.
5Point-Slope Equation of a Line
Given the slope m passing through the point
,
an equation of the line can be written in the form
6Example
- Example Find an equation of a line that has a
slope of 4 and passes through the point (-2, 3).
7Examples of Horizontal and Vertical Lines
Example Find an equation of a vertical line
that passes through the point (-2, 6).
Example Find an equation of a horizontal line
that passes through the point (-2, 6).
8Graphing Lines Using Slope-Intercept Method
Example Sketch the graph of
using the slope-intercept method.
m slope b y-intercept
9More Examples of Lines
Ex Sketch the graph of
Ex Sketch the graph of
This will be a ____________ line with an
____-intercept of -2.
This will be a _______________ line with a
__-intercept of 3.
Note This is not a function
What is the slope of the line?
What is the slope of the line?
10Summary of Lines
- General form Ax By C 0
- Vertical line x a
- Horizontal line y b
- Point-slope form y y1 m(x x1)
- Slope-intercept form y mx b
11Parallel and Perpendicular Lines
Two distinct nonvertical lines are parallel iff
their slopes are____________________.
Two distinct nonvertical lines are perpendicular
iff their slopes are _______________
_________________ of each other.
12Example-Parallel Line
Example Write an equation of the line that is
parallel to the line x y 7 and passes through
the point (-3, 2).
13Example-Perpendicular Line
Example Write an equation of the line that is
perpendicular to the line x y 7 and passes
through the point (-3, 2).
14Another Example Parallel and
Perpendicular Lines
Find the general form equation of the line that
passes through and is
a) parallel to b) perpendicular to
15Homework
Section P.2 pages 16- 17 1-5 odd, 15-19 odd,
23-29 odd, 35, 37, 39, 43, 57-61 odd, 69, 71