2.4 Writing Equations of Lines

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2.4 Writing Equations of Lines

• p. 91

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• Weve learned to graph given an equation.
• Now well learn to write the equation given the
  graph
• There are three ways.
• It all depends on what information you are given
  as to which process you use.

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Given the slope, m, and the y-intercept, b, use
the equationymxb

• The y-intercept is -3
• b-3
• The slope is 4/3
• The equation is
• y 4/3x 3

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Use Point Slope FormIf you are given slope, m,
and a point (x1,y1) on the line

• y y1 m ( x x1)

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Write an equation of a line containing the point
(1,2) with slope of -1/2.

• Use (x1,y1) (1,2) m -1/2
• y 2 -1/2 ( x 1)
• Now you can simplify to the slope intercept form
• y 2 -1/2 x ½
• y -1/2 x 5/2

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If you are given two points on the line

• Find the slope using the two points
• Then plug this slope and either one of the points
  into the point slope formula.

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Given two points (-2,2) (3,7)

• Find the slope
• m1
• Plug this slope and one of the points into the
  point slope formula.
• y 2 1 ( x (-2))
• y 2 x 2
• y x 4 (put the equation into slope
  intercept form)

(3,7)
(-2,2)
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Direct Variation

• 2 variables X Y show direct variation provided
  y kx k ? 0.
• The non-zero constant k is called the constant of
  variation, y is said to vary directly with x.
• The graph of ykx is a line thru the origin.

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The variables x y vary directly, y 12 when
x 4. Write and graph an equation relating x
y.

• Use x y to find the constant of variation
• y kx
• 12 k4
• 3 k
• The direct variation equation is y 3x
• This is what you MUST write as the answer!

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Graph y 3x
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In the same direct variation equation, when x5,
find the value of y.

• y 35
• y 15

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Assignment