2.4 Writing Equations of Lines

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					   2.4 Writing
Equations of Lines
       p. 91
• We’ve learned to graph
  given an equation.
• Now we’ll 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.
Given the slope, m, and the y-
intercept, b, use the equation
            y=mx+b
                 •The y-intercept is -3
                 •b=-3
       3         •The slope is 4/3

   4             •The equation is:
                 •y = 4/3x – 3
     Use Point Slope Form:
If you are given slope, m, and a
     point (x1,y1) on the line



•y – y1 = m ( x – x1)
   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
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.
Given two points (-2,2) & (3,7)
• Find the slope:
• m=1
• Plug this slope and one of
  the points into the point             (3,7)
  slope formula.
                               (-2,2)
• y – 2 = 1 ( x – (-2))
• y–2=x+2
• y = x + 4 (put the
  equation into slope
  intercept form)
          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 y=kx is a line thru the
  origin.
    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!
Graph y = 3x
  In the same direct variation
  equation, when x=5, find the
           value of y.

• y = 3*5
• y = 15
Assignment