Linear Equations

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Linear Equations
Vertical Line Slope is undefined x-intercept is
(a,0)
x a
Horizontal l Line Slope is 0 y-intercept is
(o,b)
y b
Slope Intercept form of a Line Slope is m
y-intercept is (o,b)
y mx b
Standard Form Slope is A/B x- intercept is
(C/A,0) y-intercept is (0,C/B)
Ax By C
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Slope of a Line
Rise
change in y - values
Slope

change in x - values
Run
where (x1 , y1) and (x2 , y2) are any two points
on the line.
Possibilities for a Lines Slope
Line rises from left to right m gt 0
Line is horizontal m 0
Line falls from left to right m lt 0
Line is vertical m is undefined
Two lines are perpendicular is the product of
their slopes equals -1.
Two non-vertical lines with the same slope are
parallel.
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Examples
Example 1 Find the equation of line with
slope -4/3 and y- intercept (0, 4).
Example 2 Find the equation of line through
(-2, 6) and with slope -2
Example 3 Find the equation of line
perpendicular to the 2x 3y 8
and has Y-intercept (0,-2)
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Point-Slope Form a Line

• Definition of slope is used to obtain the
  Point-Slope Form of a Line.
• Can be used to fine the equation when the slope
  and one point is known.
• For example

m
where (x1 , y1) and m are known can be written as
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Finding the Equation of a Line Given Two Points
Find the equation of line with through (2,5) and
(-1, 7)
Step 1
Find the slope of the line, using the slope
formula.
Step 2
Using either (2,5) or (-1, 7) use the definition
of slope to find the equation.
y-y1 m(x-x1)
y 5 -2/3 (x-2) y- 5 -2/3 x 4/3 y -
2/3 x 4/3 5 Y - 2/3 x 19/3
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Linear Equations
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Writing Equations of Line That Models Real Data

• Data that changes at a fairly constant rate will
  have a linear
• pattern.
• Graph of the data will be linear in nature.
• The rate of change of the data is the slope of
  the line that
• represents the data.

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Writing Equations of Line That Models Real Data
Example 1 Suppose there is a flat rate of .20
plus a charge of .10 per min to make a telephone
call. Write an equation that gives the cost y
for a call of x minutes.
Answer Y .1X .2
Q What does Graph look like ? Q What does the
y-intercept represent ?
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Writing Equations of Line That Models Real Data
Example 2 The percentage of mothers of children
under 1 year old who participated in the U.S.
labor force is shown in the table for selected
years. Find an equation that models the data.
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Writing Equations of Line That Model Real Data
Example 2 (Cont).
60 55 50 45 40 35 30 25 20 15 10
0 2 4 6 8 10 12 14 16 18 20
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Writing Equations of Line That Model Real Data
Example 2 (Cont).
1.) Choose two points that to find the slope of
the line. (0,38) (18, 59)
slope 1.17 2.) Using Slope intercept form of
line then the equation is Y 1.17X
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