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Rates of Change (Slope)

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Rates of Change (Slope) Section P.2 After this lesson, you should be able to: find the slope of a line passing through two points write the equation of a line given ... – PowerPoint PPT presentation

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Title: Rates of Change (Slope)


1
Rates of Change (Slope)
  • Section P.2

2
After 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

3
Slope of a Line
Slope
Also,
A line has the same slope everywhere.
4
Equations of Lines
To write the equation of a line, you need
  • one point
  • the slope

Remember Equations of lines are first degree
equations.
5
Point-Slope Equation of a Line
Given the slope m passing through the point
,
an equation of the line can be written in the form
6
Example
  • Example Find an equation of a line that has a
    slope of 4 and passes through the point (-2, 3).

7
Examples 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).
8
Graphing Lines Using Slope-Intercept Method
Example Sketch the graph of
using the slope-intercept method.
m slope b y-intercept
9
More 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?
10
Summary of Lines
  1. General form Ax By C 0
  2. Vertical line x a
  3. Horizontal line y b
  4. Point-slope form y y1 m(x x1)
  5. Slope-intercept form y mx b

11
Parallel 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.
12
Example-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).
13
Example-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).
14
Another Example Parallel and
Perpendicular Lines
Find the general form equation of the line that
passes through and is
a) parallel to b) perpendicular to
15
Homework
Section P.2 pages 16- 17 1-5 odd, 15-19 odd,
23-29 odd, 35, 37, 39, 43, 57-61 odd, 69, 71
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