Unit 6 Linear Equations and their Graphs - PowerPoint

							Unit 6:   Writing Linear
           Equations
                     Warm up
                      Retail Sales
A music store is offering a coupon promotion on its
CDs. The regular price for CDs is $14.With the coupon,
customers are given $4 off the total purchase. The
equation t = 14c - 4, where c is the number of CDs and
t is the total cost of the purchase, models this situation.

a.) Graph the equation.
b.) Find the total cost for a sale of 6 CDs.
         Slope-Intercept Form
     y = mx + b
  – where m is the slope
  – b is the y-intercept

Your Turn-
 Identify the slope & y-intercept
  1. y = 3x − 5
  2. y = ½ x + 3
  3. y = -2x + ¾
          Slope-Intercept Form
       y = mx + b
   – where m is the slope
   – b is the y-intercept

Your Turn-
  Identify the slope & y-intercept

   1. y = 3x − 5        The slope is 3; the y-intercept is −5
   2. y = ½ x + 3       The slope is ½ ; the y-intercept is 3
   3. y = -2x + ¾       The slope is -2; the y-intercept is ¾
      Using Slope & One Point
When given one point and the slope use the
 point in the place of x & y to find the
 equation.
                m = ¼; ( 2, 7)
                7 = ¼ (2) + b
         Using Slope & One Point
Your Turn –

1.

2.

3.

4.
       Using Slope & One Point
Your Turn –

1.

2.

3.

4.
               Using Two Points to
                Write an Equation
• When given two points first find the slope
     • (x1, y1) (x2, y2)
     • (2, 4) ( -1 , 3)
• Then plug in the slope and either point to find
  equation of the line.
     •   4 = ⅓(2) + b
     •   4= ⅔+b
     •   4-⅔=⅔-⅔+b
     •   3 ⅓ = b or ( )
   Point-Slope Form of a Linear Equation

The point-slope form of the equation of a
non-vertical line that passes through the point
(x₁, y₁) with slope m is: y - y₁ = m (x - x₁).
• Suppose you know that a line passes through the point (3, 4) with slope 2.
        –You can quickly write an equation of the line using the x- and y-coordinates
          of the point and the slope.
Graphing Using Point-Slope Form
Graph the equation :   y−5=   (x − 2)
           Writing an Equation in
             Point-Slope Form
    Use the slope and one point on the Line
                        (x₁, y₁), m
                   y - y₁ = m (x - x₁)
       m= ½, ( 2, 3)             y – 3 = ½ ( x – 2)
Your Turn:
1. m= ⅔, ( -1, 4)
2. m= ⅓, ( -2, -5)
3. m= -2, ( 5, 3)
           Writing an Equation in
             Point-Slope Form
    Use the slope and one point on the Line
                          (x₁, y₁), m
                   y - y₁ = m (x - x₁)
           m= ½, ( 2, 3)        y – 3 = ½ ( x – 2)
Your Turn:
1. m= ⅔, ( -1, 4)         y – 4 = ⅔ ( x – (-1))
2. m= ⅓, ( -2, -5)        y – (-5) = ⅓ ( x – (-2))
3. m= -2, ( 5, 3)         y – 3 = -2 (x – 5)
     Standard Form of a Linear Equation

     The standard form of a linear equation is
                    Ax + By = C
             – where A, B, and C are real numbers
             – and A and B are not both zero.

If the equation contains fractions or
decimals, multiply to write the
equation using integers (positive or
negative whole numbers).
   •To get rid of fractions, multiply through
   with the denominator.
   •To get rid of decimals, multiply through
   by 10’s. (10, 100, 1000, etc)
     Standard Form of a Linear Equation

Your Turn –


1.

2.

3.
     Standard Form of a Linear Equation

Your Turn –
1.                        2x – 3y = -15

2.                        3x + 4y = -16

3.                         4x + 10 y = 1
                      Special Graphs
 Absolute Value Equations
    are shaped like a V

Graph the function y = | x | + 1




                                         Quadratic Equations
                                          are shaped like a U

                                   Graph the function f(x) = x2 + 1.
                          Translations
A shift of a graph horizontally, vertically, or both. The result is a
   graph of the same shape and size, but in a different position.

   Below are the graphs of y = | x | and y = | x | + 2. Describe
    how the graphs are the same and how they are different.




          The graphs are the same shape. The y-intercept of the first
             graph is 0. The y-intercept of the second graph is 2.
                Graphing Translations
Graphing a Horizontal Translation
    Graph each equation by
       translating y = | x |.




                                     Graphing Vertical Translations
                                           Graph y = | x | − 1.
                                    Start with the graph of y = | x |.
                                    Translate the graph down 1 unit.
                Graphing Translations
Graphing a Horizontal Translation
    Graph each equation by
       translating y = | x |.




                                     Graphing Vertical Translations
                                           Graph y = | x | − 1.
                                    Start with the graph of y = | x |.
                                    Translate the graph down 1 unit.
   Writing an Absolute Value Equation
       A V-shaped graph that points upward or downward
           is the graph of an absolute value equation.


Write the equation for a vertical translation



Write the equation for a horizontal translation
 Writing an Equation for a Trend Line
Make a scatter plot of the data at the left. Draw a trend
 line and write its equation. Use the equation to
 predict the wingspan of a hawk that is 28 in. long.
                 Lines of Best Fit Using
                 a Graphing Calculator
The trend line that shows the relationship between two sets of data most
  accurately is called the line of best fit.

A graphing calculator computes the equation of a line of best fit using a
   method called linear regression.

The graphing calculator also gives you the correlation coefficient r, which
  tells you how closely the equation models the data.




When the data points cluster around a line, there is a strong correlation
  between the line and the data. So the nearer r is to 1 or −1, the more
  closely the data cluster around the line of best fit.