Graphing Linear Relations

Objective: To be able to find solutions for relations with two

variables and graph the solutions.

Do Now

Tell me everything you know about the point (0,3)- What is it?- What does it mean?- Tell me about its parts.

Graphing Linear Relations

A linear relation will form a straight line when graphed upon a coordinate system.

Graphing Linear Relations

Example:

61

63

71

90

87

21 + 40

23 + 40

31 + 40

50 + 40

47 + 40

21

23

31

50

47

Temperature (°F)

c + 40Chirps in 15 seconds

Graphing Linear Relations

Example 1: a. Find four solutions for the equation

y = -2x + 1. Write the solutions as ordered pairs.

Graphing Linear Relations

Example 1: a. Find four solutions for the equation

y = -2x + 1. Write the solutions as ordered pairs.x -2x + 1 y-2 -2(-2) + 1 50 -2(0) + 1 11 -2(1) + 1 -13 -2(3) + 1 -5

Graphing Linear Relations

Example 1: a. Find four solutions for the equation

y = -2x + 1. Write the solutions as ordered pairs.x -2x + 1 y-2 -2(-2) + 1 50 -2(0) + 1 11 -2(1) + 1 -13 -2(3) + 1 -5

(-2, 5), (0, 1), (1, -1), (3, -5)

Graphing Linear Relations

Example 1: a. Find four solutions for the equation

y = -2x + 1. Write the solutions as ordered pairs.

b. Graph the equation y = -2x + 1.

x -2x + 1 y-2 -2(-2) + 1 50 -2(0) + 1 11 -2(1) + 1 -13 -2(3) + 1 -5

(-2, 5), (0, 1), (1, -1), (3, -5)

Graphing Linear Relations

Example 1: a. Find four solutions for the equation

y = -2x + 1. Write the solutions as ordered pairs.

b. Graph the equation y = -2x + 1.

x -2x + 1 y-2 -2(-2) + 1 50 -2(0) + 1 11 -2(1) + 1 -13 -2(3) + 1 -5

(-2, 5), (0, 1), (1, -1), (3, -5)

Graphing Linear Relations

Example 2: a. Find four solutions for the equation

y = 4x – 3. Write the solutions as ordered pairs.

Graphing Linear Relations

Example 2: a. Find four solutions for the equation

y = 4x – 3. Write the solutions as ordered pairs.x 4x - 3 y-2 4(-2) - 3 -110 4(0) - 3 -31 4(1) - 3 13 4(3) - 3 95 4(5) - 3 17

Graphing Linear Relations

Example 2: a. Find four solutions for the equation

y = 4x – 3. Write the solutions as ordered pairs.(-2, -11), (0, -3), (1, 1), (3, 9), (5, 17)x 4x - 3 y

-2 4(-2) - 3 -110 4(0) - 3 -31 4(1) - 3 13 4(3) - 3 95 4(5) - 3 17

Graphing Linear Relations

Example 2: a. Find four solutions for the equation

y = 4x – 3. Write the solutions as ordered pairs.

b. Graph the equation y = 4x – 3.

(-2, -11), (0, -3), (1, 1), (3, 9), (5, 17)x 4x - 3 y-2 4(-2) - 3 -110 4(0) - 3 -31 4(1) - 3 13 4(3) - 3 95 4(5) - 3 17

Graphing Linear Relations

Example 2: a. Find four solutions for the equation

y = 4x – 3. Write the solutions as ordered pairs.

b. Graph the equation y = 4x – 3.

(-2, -11), (0, -3), (1, 1), (3, 9), (5, 17)x 4x - 3 y-2 4(-2) - 3 -110 4(0) - 3 -31 4(1) - 3 13 4(3) - 3 95 4(5) - 3 17

Graphing Linear Relations

Example 3: A 20 foot board is sawed into two pieces. If x and y are the measures of the two pieces, the equation x + y = 20 models the conditions.

Graphing Linear Relations

Example 3: A 20 foot board is sawed into two pieces. If x and y are the measures of the two pieces, the equation x + y = 20 models the conditions.a. Graph the equation.

10

8

6

20

0 2 4

2

4

18

16

14

12

x

y

14 16 18 206 8 10 12

Graphing Linear Relations

Example 3: A 20 foot board is sawed into two pieces. If x and y are the measures of the two pieces, the equation x + y = 20 models the conditions.a. Graph the equation.

b. Use the graph to name a solution of the equation. 10

8

6

20

0 2 4

2

4

18

16

14

12

x

y

14 16 18 206 8 10 12

Graphing Linear Relations

Example 3: A 20 foot board is sawed into two pieces. If x and y are the measures of the two pieces, the equation x + y = 20 models the conditions.a. Graph the equation.

b. Use the graph to name a solution of the equation.

c. Is (-1, 21) a solution of the equation?

10

8

6

20

0 2 4

2

4

18

16

14

12

x

y

14 16 18 206 8 10 12

Graphing Linear Relations

Assignment: 20 – 54 even, 56 – 70 all.Page 389