1. Equations of Linear Relationships

2. Linear Equation - an equation that forms a line when graphed. Y=12X
X is the independent variable (input)
Y is the dependent variable (output)
to graph an equation make a table of ordered pairs

3. Rule
Output
Input
Rule
Output
Ordered Pair
y = 2x + 9 x
2x + 9 y
(x, y) –1
Input 1 2
Choose any four values for x and then solve for y.
Use small values to keep graph small and calculations easy

4. Make a table for x = -1, 0, 1, and 2, and graph the resulting ordered pairs.
EX1) y = x – 4 y 4
Ordered
Pair
Input
Rule
Output 2 x
x – 4 y
(x, y) x –4 –2 2 4 –1
–1 – 4 –5
(–1, –5) –2
(2,- 2)
0 – 4 –4
(0, –4)
(1, –3)
(0, –4) –4 1
1 – 4 –3
(1, –3)
(–1, –5) 2
2 – 4 –6 -2
(2, -2) –8
–10

5. Make a table for x = -1, 0, 1, and 2, and graph the resulting ordered pairs.
EX2) y = 2x – 3
Ordered
Pair
Input
Rule
Output y 4 x
2x – 3 y
(x, y) 2
(2, 1) –1
2(–1) – 3 –5
(–1, –5)
2(0) – 3 –3
(0, –3) x –4 –2 2 4
(1, –1) 1
2(1) – 3 –1 –2
(1, –1)
(0, –3) 2
2(2) – 3 1
(2, 1) –4
(–1, –5) –6 –8
–10

6. Ex3) y = 4x + 1 –2 –4 2 4 (1, 5) Input Rule Output Ordered Pair x–2 –4 2 4
(1, 5)
Input
Rule
Output
Ordered Pair x
4x + 1 y
(x, y)
(0, 1) –1
4(–1) + 1 –3
(–1, –3)
4(0) + 1 1
(0, 1)
(–1, –3) 1
4(1) + 1 5
(1, 5)

7. EX2) y = 3x + 1. Input Rule Output Ordered Pair x 3x + 1 y (x, y) –1
3(–1) + 1 –2
(–1, –2) x y
3(0) + 1
(0, 1)
(1, 4) 1 4 1
3(1) + 1 4
(1, 4) 2
(0, 1) –4 –2 2 4 –2
(–1, –2) –4

8. Essential Question
How can linear relationships be represented?

9. Equations of Linear Relationships
Date _____________
Equations of Linear Relationships

10. Linear Equation - an __________ that forms a ______ when graphed. Y=12X
X is the independent variable (______)
Y is the dependent variable (________)
to graph an equation make a _______ of ordered pairs

11. y = 2x + 9 Choose any four values for __ and then solve for __.
Input
Rule
Output
Ordered Pair
y = 2x + 9 x
2x + 9 y
(x, y) –1 1 2
Choose any four values for __ and then solve for __.
Use small values to keep graph small and calculations easy

12. Make a table for x = -1, 0, 1, and 2, and graph the resulting ordered pairs.
EX1) y 4
Ordered
Pair
Input
Rule
Output 2 x
x – 4 y
(x, y) x –4 –2 2 4 –2 –4 –6 –8
–10

13. Make a table for x = -1, 0, 1, and 2, and graph the resulting ordered pairs.
EX2) y =
Ordered
Pair
Input
Rule
Output y 4 x
2x – 3 y
(x, y) 2 x –4 –2 2 4 –2 –4 –6 –8
–10

14. Ex3) y = x y –2 –4 2 4
Input
Rule
Output
Ordered Pair x y
(x, y)

15. EX4) y = Input Rule Output Ordered Pair x y (x, y) 4 2 –4 –2 2 4 –2 –4–4 –2 2 4 –2 –4

16. Essential Question
How can linear relationships be represented?