Section 2.2 Graphing Linear Equations

							Section 2.2
Graphing Linear Equations
   Solutions of Equations in Two Variables
   Graphing from a Table of Points
   Graphing from the Intercepts
   Horizontal & Vertical Lines
   Linear Models
Solutions to Equations
   A solution to an equation in two variables is any
    ordered pair of numbers (a,b) that makes a true
    statement when substituted into the equation.
   Example: (2,7) is a solution to y = 3x + 1
                            because 7 = 3(2) + 1
   You can find solutions by choosing a value for one
    variable, then solving the equation for the other variable
   Example: For y = 3x + 1 Let x = 9
                then y = 3(9) + 1 = 28
                and this solution is shown by (9,28)
Class Exercise – Finding Solutions
      1
 y   x5                          1
                               y   6  5
                                    3
      3                        y  2  5
   a.) What is the solution
                               y 3
     when x = 6 ?                              1
                                          5   x5
                                               3
                                          5     5
   b.) What is the solution
                                              1
    when y = 5 ?                          0  x
                                              3
                                          0x
Why graph equations?
   Consider the equation with two variables,
        y  2x  3
   What will the solutions for this equation look like?
       Ordered pairs: (x-value, y-value) (0,-3) for example
   How many solutions are there?
       Infinitely many
Definitions
• The graph of an equation
  is the set of all points (x, y) on the rectangular
  coordinate system whose coordinates satisfy the
  equation. It is the visual solution set for the equation.

• A linear equation in two variables
  is an equation that can be put into the form Ax+By=C
  (A and B can’t both be zero).
  The graph of a linear equation is always a line.
Rough Graphing
   Plan to use about
    1/6 of a sheet
    of paper                     15
                                 10
                                  5
   Neatly draw the       -15 -10 -5 0 5 10 15
                                   -5
    x-axis and y-axis             -10
                                  -15
   Label every 5 units
Class Exercise – Graphing an Equation

               1
          y   x5
               3
You already found two points: (6,3) and (0,5)
 Find another point when x = -3

 Use these 3 points to rough graph the equation
Graphing using                                               1
                                                        y   x5
The Intercept Method                    (“Cover-up Method”)  3
   The y-intercept of a line is the point (0, b), where
    the line intersects the y-axis.
       To find b, substitute 0 for x in the equation of the line and
        solve for y.
   The x-intercept of a line is the point (a, 0), where
    the line intersects the x-axis.
       To find a, substitute 0 for y in the equation of the line and
        solve for x.
   Another Example:         7x – 14y = 35
In-Class Exercises:
   Make a table of 3 points and use it to graph
           1   5
       y  x
           2   2
   Graph using intercepts:

       4 x  3 y  12
How would you graph the following
equations?

     y3

      x2
Horizontal & Vertical Lines
   Is y = 3 a Linear Equation?       Is x = 2 a Linear Equation?
   0x + y = 3    Yes!                x + 0y = 2 Yes!




             Graph:    x = -5         y=-4       y=0
  Horizontal and Vertical Lines

If a is any real number:
The graph of x = a is a vertical line with x-intercept (a, 0)
If a is 0, ( x = 0 ) the line is the y-axis.

If b is any real number:
The graph of y = b is a horizontal line with y-intercept (0, b)
If b is 0, ( y = 0 ) the line is the x-axis.
Linear Models
   We can use linear equations to mathematically model some real-life
    situations. This way we can use observations about what happened in the
    past to predict what might take place in the future.
                                                      c = 5 + .25n
   Exercise
56. TELEPHONE COSTS                                   (0,?) -> (0,5)
     In a community, the monthly
     cost of local telephone service                  (10,?) -> (10,7.5)
     is $5 per month, plus 25¢ per call.

a.Write a linear equation that gives the cost c for
     a. person making n calls.

b. Then graph the equation. (need 2 points)

c. Use the graph to estimate the cost of service in
      a month when 20 calls were made.
What Next?
   Present Section 2.3
    Rate of Change & Slope of a Line




   Accessing these Powerpoint Slides from the Internet:
    http://faculty.rcc.edu/vandewater/Section02_2.ppt
    Click on Open