1. Graphs, Relations and Functions
Cornell Notes #16

2. Graphing Linear Equations
Example
Step 1
Step 2
Find ordered pair (x, y), that when substituted into the equation, makes the equation true.
Find three ordered pairs that are solutions to the linear equation.
4x + 2y = -8
Note: substitute x=0, then y=0, and then a number you choose for the third value.
Substitute 0 for x. So, 4 (0) + 2y = -8
0 + 2y = then, divide both sides by 2
2y = then, simplify
y= so 1st coordinate point is
(0, -4)
Substitute 0 for y. So, 4x + 2(0) = -8

3. Step 2 continued
Step 3
4x + 0 = then, divide both sides by 4
4x = then simplify
x= So the 2nd coordinate point is
(-2, 0)
Choose your own number. I chose x=2..So,
4(2) + 2y = -8 Substitute in for x
8+2y=-8 then, subtract 8 from each side
y= then, simplify
0 +2y = then, divide both sides by 2
2y = simplify
y = -8 So the 3rd coordinate point is
(2, -8)

4. Graph paper project
Overview

5. Practice:
Work problem together
4x + 3y = 12
Make a 4 quadrant worksheet.
Draw, label x axis, 1-10
Draw , label y axis 1-10
Label quadrants
Label coordinate pair in each quadrant
Example: quadrant I (x, y) is (+, +)
Work x=0 in quadrant I
Work y=0 in quadrant II
Work x=___ in quadrant III
Write table in quadrant IV

6. Independent Practice
Set up your paper and work out the following linear equation.
4x + 3y =18
X-9y=-72
6x+y=21
2x-5y=0

7. What makes a pattern linear or nonlinear?
Linear and Nonlinear Relations
What does linear mean?
There is a common difference between terms: 5, 10,15, 20 difference is 5
If the rate of change (y/x) is constant, the relationship is linear.
A straight line.

8. This table represents a function.
How do I find if the relationship between x and y is linear?
Find the differences between the y’s
Move from -4 to -3 on the number line, how far did you move? 1
Between -3 and -1 is 2
Between -1 and 2 is 3
Between 2 and 6 is 4
Now find the differences between the x’s x y -5 -4 -3 1 -1 7 2 15 6

9. This table represents a function.
How do I find if the relationship between x and y is linear?
Are the y/x the same for each row?
Now find the differences between the x’s
Between -5 and -3 is 2
Between -3 and 1 is 4
Between 1 and 7 is 6
Between 7 and 15 is 8
½, 2/4, 3/6, 4/8
All these fractions reduce to ½ so the relationship is linear. x y -5 -4 -3 1 -1 7 2 15 6

10. Is the relationship between x and y linear or nonlinear?
Independent Practice
Is the relationship between x and y linear or nonlinear? x y -2 -9 -5 3 1 4 7 9

11. Application
Jonny just bought a computer that came with 4 games already installed on it. Each week, he downloads 2 more computer games.
Write an equation that represents the number of games.
Make a table for 5 weeks, and number of games each week.
Graph your answer.