Rates of Change (Slope)

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Rates of Change (Slope)

• Section P.2

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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

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

• one point
• the slope

Remember Equations of lines are first degree
equations.
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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
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Example

• Example Find an equation of a line that has a
  slope of 4 and passes through the point (-2, 3).

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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).
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Graphing Lines Using Slope-Intercept Method
Example Sketch the graph of
using the slope-intercept method.
m slope b y-intercept
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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?
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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

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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.
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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).
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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).
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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
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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