SWBAT

1
SWBATdetermine whether functions are linear
Thurs, 10/28/10

• Agenda
• WU (10 min)
• Review hw1 (10 min)
• Writing linear equations (25 min)
• Warm Up
• Graph x 2y 5 using a table of values
• (Hint solve for y first!)
• HW2 Writing Linear Equations

2
Graph x 2y 5
First Step Solve for y (write y as a function
of x)
x 2y 5 2y -x 5
3
Second Step Make a Table of Values
x y (x, y)
-2 -3.5 (-2, -3.5)
-1 -3 (-1, -3)
0 -2.5 (0, -2.5)
1 -2 (1, -2)
2 -1.5 (2, -1.5)
4
Graphing Horizontal Vertical Lines
When you are asked to graph a line, and there is
only ONE variable in the equation, the line will
either be vertical or horizontal. For example
Graph x 3
Since there are no yvalues in this equation, x
is always 3 and y can be any other real number.
y 2
Graph y 2
Since there are no xvalues in this equation, y
is always 2 and x can be any other real number.
x 3
5
SWBATdetermine whether functions are linear
Fri, 10/29/10

• Agenda
• WU (10 min)
• Binder Check (10 min)
• Writing linear equations (25 min)
• Warm Up On one graph paper square
• 1. Graph x -6
• 2. Graph y 1
• HW2 Writing Linear Equations

6
Graph x -6
Since there are no yvalues in this equation, x
is always -6 and y can be any other real number.
y 1
Graph y 1
Since there are no xvalues in this equation, y
is always 1 and x can be any other real number.
x -6
7
Binder Check

1. Exchange binders with the person next you
2. You will be grading each others binder

8
Writing Linear Equations

• Infinity HS
• Ms. Sophia Papaefthimiou

9
Linear Equation
C is called the constant. A constant is a
number. Ax and By are variable terms.

• The equation of a line is often written in the
  form Ax By C
• This is called standard form where A 0, A and B
  are not both zero, and A, B, and C are integers
  whose greatest common factor is 1.
• Examples
• 3x 2y 5
• A 3, B 2 and C 5
• x -6
• A 1, B 0 and C -6

10
Identify Linear Equations

• Directions Determine whether each equation is
  linear. If yes, write the equation in standard
  form.
• Ex1 y 5 2x
• 2x y 5
• The equation is in standard form where A 2,
  B 1, and C 5. Yes, this is a linear
  equation.

First rewrite the equation so both variables are
on the same side of the equation (Standard Form
Ax By C)
11
Identify Linear Equations (contd)

• Ex2 2xy 5y 6
• Since the term 2xy has two variables, the
  equation cannot be written in the form Ax By
  C. Therefore, this is not a linear equation.
• Ex3 y x2 4
• Since the term x2 is squared, the equation
  cannot be written in the form Ax By C.
• Therefore, this is not a linear equation.

12
SWBATwrite algebraic equations from data
Mon, 11/4/10

• Agenda
• WU (10 min)
• Notes 4 slides rate of change (10 min)
• OYO problems (15 min)
• Review hw2 (10 min)
• WU Write the equation in standard form
• HW3 Algebraic Rules

13
Identify Linear Equations (contd)(HW Prob 4)

• Ex4
• The equation is in standard form where A 2, B
  -1, and C 6. Yes, this is a linear equation.
  

To write the equation with integer coefficients,
multiply each term by 3.
14
Linear or Non-linear Function

• For a function to be linear, the rate of change
  must be constant, meaning the change in the
  y-values must be constant and the change in the
  x-values must be constant.
• Ex1 Does the table below show a linear
  relationship?

x y
1 0
2 2
3 4
4 6
Yes, the rate of change is constant (the change
in the y is constant, the change in the x is
constant.) Thus, the function is linear.
15
Linear or Non-linear Function (contd)

• Ex2 Does the table below show a linear
  relationship?

x y
1 6
2 12
3 18
4 24
Yes, the rate of change is constant (the change
in the y is constant, the change in the x is
constant.) Thus, the function is linear.
16
Linear or Non-linear Function (contd)

• Ex3 Does the table below show a linear
  relationship?

x y
12 -4
9 1
6 6
3 11
0 16
Yes, the rate of change is constant (the change
in the y is constant, the change in the x is
constant.) Thus, the function is linear.
17
Linear or Non-linear Function (contd)

• Ex4 Does the table below show a linear
  relationship?

x y
-3 10
-1 12
1 16
3 18
5 22
No, this rate of change is not constant. Thus,
the function is not linear.
18
OYO Problems

• Write the following equations in standard form,
  Ax By C
• x y 8
• 3. 3x 9y 15 (Hint The GCF of 3, 9, and 15
  is not 1)