Linear Equations in Standard Form

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Linear Equations in Standard Form

• Todays goal writing standard form equations for
  lines
• (and a few horizontal vertical lines at the end)

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First, lets review!

• Given the equation y 3 -4(x 1)
• What is the slope of the line?
• What is one point on the line?
• Graph the line.
• Slope -4 point (1, -3) graph by plotting (1,
  -3) and going down 4 and right 1 to the next
  point.

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Review problem 2

• Write a point-slope equation for the line through
  (1, 4) (-2, -5), then change your equation to
  slope-intercept form.
• y 4 3(x 1) or y 5 3(x 2)
• y 3x 1

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Lets look at a graph

• Write a point-slope equation.
• Write a slope- intercept equation.

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Lets look at a graph

• Write a point-slope equation. y
  1 -3(x 1) or y 2 -3(x 2)
• Write a slope- intercept
  equation. y -3x 4

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Today the 3rd form of linear equations!

• Standard Form ax by c
• a, b, c dont mean anything (not slope or
  intercepts)
• So we cant just write a standard form equation
  from information. We need to write a point-slope
  or slope-intercept equation, then move things
  around to be standard form ? get x y on one
  side, constant on the other.

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First example

• Start with a slope-intercept equation. y -2x
  4
• Move the -2x to the left side. (2x to both
  sides) 2x 2x
• Get a standard form equation. 2x y 4

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Second example

• Start with a point-slope equation. y 2
  3(x 5)
• Change to slope-int. form. (Dist. Prop., solve
  for y) y 3x - 17
• Move the 3x to the left side. (-3x to both
  sides) -3x -3x
• Get a standard form equation. -3x y -17

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Steps for your notes

• Write a point-slope equation.
• Use Distributive Property solve for y to change
  the equation to slope-intercept form.
• Move the x term to the front by doing its
  opposite to both sides.
• (If you start with a slope-intercept equation,
  you only need to do the last step.)

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Why Standard Form?

• Its easy to graph by finding the x-intercept
  y-intercept.
• Its easy to use in word problems.
• Like point-slope form, theres more than one
  correct standard form equation for a line.

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Write a Standard Form equation for the line
(start in another form)

• You can use the points (0, 2)
  (2, 1)

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Write a Standard Form equation for the line
(start in another form)

• y 1/2x 2 - 1/2x y 2

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Write a Standard Form equation for the line
(start in another form)

• You can use the points (1, 4)
  (4, -5)

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Write a Standard Form equation for the line
(start in another form)

• y 4 -3(x 1) y 4 -3x 3
  y -3x 7 3x y 7

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Word problems with Standard Form

• Use standard form when two things are changing to
  get a total.
• Example Cookies cost 2 each, and brownies are
  3 each. You have 24 to spend on cookies
  brownies.
• 2c 3b 24
• (or 2x 3y 24)
• (you can graph by finding x- y-intercepts like
  we did in Chapter 4)

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Equations for Horizontal Lines

• Horizontal lines have slope 0
• All ys are the same, so equations are y
• y 4
• y -2

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Write an equation for the line

• 1) the line below 2) line through
  (0, -5) (4, -5)

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Write an equation for the line

• 1) the line below 2) line through
  (0, -5) (4, -5) y 0 y -5

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Equations for Vertical Lines

• Vertical lines have undefined slope
• All xs are the same, so equations are x
• x -5
• x 1

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Write an equation for the line

• 1) the line below 2) line through
  (3, 5) (3, 1)

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Write an equation for the line

• 1) the line below 2) line through
  (3, 5) (3, 1)
• x -2 x 3

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Assignment time!

• Due tomorrow
• p314 1-4, 11-27 odd, 40, 41, 45-48