Equations of Linear Relationships

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

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

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

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

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)

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

Essential Question How can linear relationships be represented?

Equations of Linear Relationships Date _____________ Equations of Linear Relationships

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

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

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

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

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

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

Essential Question How can linear relationships be represented?