1. Graphing Linear Relations
Objective: To be able to find
solutions for relations with two
variables and graph the solutions.

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

3. Graphing Linear Relations
A linear relation will form a straight line when
graphed upon a coordinate system.

4. Graphing Linear Relations
Example: Chirps in 15 c + 40 Temperature
seconds (°F)
21 21 + 40 61
23 23 + 40 63
31 31 + 40 71
50 50 + 40 90
47 47 + 40 87

5. Graphing Linear Relations
Example 1: a. Find four solutions for the equation
y = -2x + 1. Write the solutions as ordered pairs.

6. 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 5
0 -2(0) + 1 1
1 -2(1) + 1 -1
3 -2(3) + 1 -5

7. 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, 5), (0, 1), (1, -1), (3, -5)
-2 -2(-2) + 1 5
0 -2(0) + 1 1
1 -2(1) + 1 -1
3 -2(3) + 1 -5

8. 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, 5), (0, 1), (1, -1), (3, -5)
-2 -2(-2) + 1 5
0 -2(0) + 1 1
1 -2(1) + 1 -1
3 -2(3) + 1 -5
b. Graph the equation y = -2x + 1.

9. 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, 5), (0, 1), (1, -1), (3, -5)
-2 -2(-2) + 1 5
0 -2(0) + 1 1
1 -2(1) + 1 -1
3 -2(3) + 1 -5
b. Graph the equation y = -2x + 1.

10. Graphing Linear Relations
Example 2: a. Find four solutions for the equation
y = 4x – 3. Write the solutions as ordered pairs.

11. 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 -11
0 4(0) - 3 -3
1 4(1) - 3 1
3 4(3) - 3 9
5 4(5) - 3 17

12. 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 -11 (-2, -11), (0, -3), (1, 1), (3, 9), (5, 17)
0 4(0) - 3 -3
1 4(1) - 3 1
3 4(3) - 3 9
5 4(5) - 3 17

13. 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 -11 (-2, -11), (0, -3), (1, 1), (3, 9), (5, 17)
0 4(0) - 3 -3
1 4(1) - 3 1
3 4(3) - 3 9
5 4(5) - 3 17
b. Graph the equation y = 4x – 3.

14. 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 -11 (-2, -11), (0, -3), (1, 1), (3, 9), (5, 17)
0 4(0) - 3 -3
1 4(1) - 3 1
3 4(3) - 3 9
5 4(5) - 3 17
b. Graph the equation y = 4x – 3.

15. 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.

16. 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. y
20
a. Graph the equation. 18
16
14
12
10
8
6
4
2
x
0 2 4 6 8 10 12 14 16 18 20

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. y
20
a. Graph the equation. 18
16
14
b. Use the graph to name a 12
solution of the equation. 10
8
6
4
2
x
0 2 4 6 8 10 12 14 16 18 20

18. 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. y
20
a. Graph the equation. 18
16
14
b. Use the graph to name a 12
solution of the equation. 10
8
6
4
c. Is (-1, 21) a solution of the 2
equation? x
0 2 4 6 8 10 12 14 16 18 20

19. Graphing Linear Relations
Assignment: 20 – 54 even, 56 – 70 all.
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