Functions and Linear Equations

1
Functions and Linear Equations
2

• Up to now, we have been solving equations with
  one variable
• (Ex 2n 4 10)
• Now we will be solving equations with 2 variables
  (Ex y 3x - 2)

3

• The solution to an equation with two variables
  will have two answers, one for each variable. The
  solution is usually written as an ordered pair
  (x,y). This ordered pair can then be graphed. If
  the graph for an equation is a straight line,
  then the equation is called a linear equation.

4

• The x value is called the input value. You can
  choose any values for the input value. The set of
  x values that solve the equation is called the
  domain.
• The y value is called the output value. It is the
  answer you get when you replace the x value with
  a given number. The set of y values that solve
  the equation is called the range.

5
Example y 3 x

• I can choose values for x to solve the equation.
• If I choose x 2, then y will equal 5 because 5
  3 2.
• If I choose x 0, then y will be equal to 3
  because 3 3 0.

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• This is easier to see when it is set up in a
  chart.

X 3 x Y (x,y)
2 3 2 5 (2, 5)
1 3 1 4 (1, 4)
0 3 0 3 (0, 3)
-1 3 (-1) 2 (-1, 2)
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• All the x values (2, 1, 0, -1) are the domain.
• All the y values (5, 4, 3, 2) are the range.