Linear Equations Review

1
Linear Equations Review

• Chapter 5

Chapters 1 2
2
What you should know aboutLinear equations
Given ANY linear equation you should be able to
identify

• Slope
• Y-intercept
• X-intercept
• What does the graph look like?
• Parallel slope
• Perpendicular slope

3
Equation Forms

• y mx b
• Ax By C
• y b
• x a

• Slope Intercept
• Standard
• Horizontal
• Vertical

4
Slopes
Negative
Positive
Horizontal
Vertical
5
Can you run through the linear equation
information
3x4y24 y 1/2x-7 y 5 x 6
6
Given any linear equation, one should be able to
3x4y24
identify

1. Standard
2. Falling
3. -3/4
4. 6
5. 8
6. -3/4
7. 4/3

• The Equation Form
• Direction
• Slope
• y-intercept
• x-intercept
• Parallel Slope
• Perpendicular Slope

7
Given any linear equation, one should be able to
y 1/2x-7
identify

1. Slope intercept
2. Rising
3. 1/2
4. -7
5. - -7/(1/2) 14
6. 1/2
7. -2

• The Equation Form
• Direction
• Slope
• y-intercept
• x-intercept
• Parallel Slope
• Perpendicular Slope

8
Given any linear equation, one should be able to
y 5
identify

1. Horizontal line
2. horizontal
3. 0
4. 5
5. Does not exist
6. 0
7. undefined

• The Equation Form
• Direction
• Slope
• y-intercept
• x-intercept
• Parallel Slope
• Perpendicular Slope

9
Given any linear equation, one should be able to
x 6
identify

1. Vertical line
2. verticle
3. undefined
4. Does not exist
5. 6
6. undefined
7. 0

• The Equation Form
• Direction
• Slope
• y-intercept
• x-intercept
• Parallel Slope
• Perpendicular Slope

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To graph a line

• Intercepts
• Identify the intercepts
• Plot the intercepts
• Draw the line

• Point-slope
• Identify a point on the line and the slope
• Plot the point
• Count the slope Rise/Run

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Graph using intercepts y -3x 7

• y-int -7
• x-int 7
• -3

(-7/3,0)
(0,-7)
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Graph using intercepts y -3x 7

• point (0, -7)
• slope -3 / 1

up 3 back 1
(0,-7)
down 3 over 1
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The slope formula

• m y1 y2
• x1 x2

• This is really the same at the point-slope
  equation
• m(x1 x2) y1 y2
• y1 y2 m(x1 x2)

14
Find the slope given 2 points (-1,1) (2,3)

• m 3 1
• 2 -1
• m 2
• 3

• m 1 3
• -1 2
• m -2 2
• -3 3

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Now write the equation (-1,1) (2,3)

• m 3 1
• 2 -1
• m 2
• 3

• y1 y2 m(x1 x2)
• y 3 2/3 (x 2)
• y 2/3 x 4/3 9/3
• y 2/3 x 5/3

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If you have two points you can find the
linesometimes the challenge is knowing what you
have.

• Given
• The origin
• The y-intercept
• The x-intercept
• A line parallel to the x-axis
• A line parallel to the y-axis

• You have
• the point (0,0)
• the point (0,y)
• the point (x,0)
• the slope m 0
• eqn is y ____
• The slope m undefined
• eqn is x ____

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Parallel Perpendicular II

• Parallel slopes are equal
• m original
• m mo

• Perpendicular slopes are opposite reciprocals
• m original
• m -1 / mo

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Linear equation parts
Slope Intercept Standard Horizontal Vertical
Equation y mx b Ax By C y b x a
Slope m -A B 0 undefined
y intercept b C B b does not exist
x - intercept -b m C A does not exist a
parallel slope m -A B 0 undefined
perpendicular slope __ -1 m B A undefined 0
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Given 3x 4y 12

• Find the line to the given line that passes
  through (-2, 5).

• Find the line __ to the given line that passes
  through (-2, 5).

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Given 3x 4y 12

• Find the line to the given line that passes
  through (-2, 5).

• Find the line __ to the given line that passes
  through (-2, 5).

If the line is parallel then the slope must be
the same so the linear equation will look like
3x 4y q
If the line is perpendicular then the slope must
be the opposite reciprocal so the linear equation
will look like -4x 3y q
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Given 3x 4y 12

• Find the line to the given line that passes
  through (-2, 5).
• 3x 4y ___
• 3(-2) 4(5) ___
• -6 20 14

• Find the line __ to the given line that passes
  through (-2, 5).
• -4x 3y ___
• -4(-2)3(5) ___
• 815 23

3x 4y 14
-4x 3y 23
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Given y 2x - 12

• Find the line to the given line that passes
  through (-2, 5).
• Slope 2 therefore
• m 2

• Find the line __ to the given line that passes
  through (-2, 5).
• Slope 2 therefore
• m__ -1/2

y 2x b
y -1/2 x b
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Given y 2x - 12

• Find the line to the given line that passes
  through (-2, 5).

• Find the line __ to the given line that passes
  through (-2, 5).

y 2x b 5 2(-2) b b 9
y -1/2 x b 5 -1/2 (-2) b b 4
y -1/2 x 4
y 2x 9
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The alternative calculation is to using the point
slope form of a linear equation y y1 m(x
x1)

• Once you identify the desired slope, you have m

• then you can substitute the point value for
  (x1,y1)

y -3x 7

• perpendicular through (1,2)

• parallel through (1,2)

• y 2 1/3(x 1)

• y 2 -3(x 1)

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Find (e,f)
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remember if you can find the blue line
you can find the y - intercept
then consider the reflection
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Find t

• Select t so that the triangle with vertices ( -4,
  2 ), ( 5, 1 ), and (t,-1) a right triangle with
  the right angle at (t,-1).

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Find t
Right angle

• Select t so that the triangle with vertices ( -4,
  2 ), ( 5, 1 ), and (t,-1) a right triangle with
  the right angle at (t,-1).

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Switching gears

• Parametric equations of the line p. 69