Equations of Lines (rearranging the furniture)

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Equations of Lines(rearranging the furniture)
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Three Forms of Linear Equations

• There are three different forms of the equation
  of a line.
• Two are for show
• slope-intercept equation of a line y mx b
• standard equation of a line Ax By C
• And one is a workhorse
• point-slope equation of a line y y1 m(
  x x1)

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Point-slope Equation of a Line

• The point-slope equation of a line y y1 m(
  x x1)
• is used to figure out the equation of a line
• when you are given a point and the slope.
• You never give your answer in point-slope form.

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Slope-intercept Equation of a Line

• The slope-intercept equation of a line y mx
  b
• is great for graphing.
• m is the slope of the line
• (0, b) is the y-intercept of the line
• You frequently are asked to give your answer in
  point-slope form.

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Standard Equation of a Line

• The standard equation of a line Ax By C
• is mainly for show.
• You frequently are asked to give your answer in
  standard form.

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Slope-intercept Form

• If they tell you that the slope is
• And the y-intercept is (0, 5)
• The slope intercept equation is y x 5

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From slope-intercept to Standard Form

• The slope intercept equation is y x 5
• To write that in standard form, first multiply
  each term by the LCD.
• 4y 7x 20
• Then rearrange the furniture.
• 7x 4y 20
• 7x 4y 20

Make x positive
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From Standard to slope-intercept Form

• What if they ask you to graph
• 7x 4y 20
• Then rearrange the furniture solve for y
• 4y 7x 20
• y x 5
• Now you know the slope and the y-intercept and
  its easy to graph!

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Equations of lines
Point-slope never the form of an
answer. Slope-intercept Great for graphing. May
be requested for an answer. Standard form
Frequently requested for answers.