1. LESSON 2.04: Graphing Linear Relations using a Table of Values MFM1P
Graphing Linear Equations

2. Before we begin the lesson, evaluate each equation using the given value.
(a) C= 4n + 20; when n = 3
(b) C = 25n + 220; when n = 50
(c) C = 2.5n + 30; when n = 17

3. Graphing Linear Equations

4. Leering Goals
Students will graph linear equations using a table.

5. Vocabulary
A linear equation you can plug x vertically… Given an equation that y=_x or x=_y if you substitute values for x or y, and plot a graph it will make a line!
The solution to linear equations are ordered pairs for you to use on your graph!

6. What is a Linear Equation?
A linear equation is an equation whose graph forms a straight line.
Linear equations are usually shown on a coordinate plane AKA Cartesian Plane
Real life situations of linear equations include the stock market as well as the payments of a car.

7. Example #1 This is an example of a linear equation y = x + 8
In this case whatever x is plus 8 will give you the value of y

8. Graphing
Since the results of a linear equations can be expressed as ordered pairs, the linear equation can be graphed.
There are a number of ways to find the solution to a linear equation…for today’s lesson we will look at creating a table of the solutions…

9. Tables
To create a table of solutions to a linear equation do the following:
Choose a minimum of 3 values for x
Substitute the values of x into the linear equation
Simplify to find the value of y
Write the solutions as ordered pairs
Let’s look at an example…

10. Example #2 y = 2x – 1 x y = 2x – 1 y (x, y) y = 2(0) – 1 - 1 (0, - 1)
1. Choose a minimum of 3 values for x
y = 2x – 1 x
y = 2x – 1 y
(x, y)
y = 2(0) – 1
- 1
(0, - 1) 1
y = 2(1) – 1
(1, 1) 2
y = 2(2) – 1 3
(2, 3)
2. Substitute the value of x into the equation
4. Write as an ordered pair
3. Simplify to determine the value of y

11. ? Comments How do you choose the value of x?
You can use any number for the value of x…however, you can make your life easy by choosing -1, 0, and 1, because you can do mental math and they are easy to graph.
You choose a minimum of 3 numbers because when graphed the expected result is a straight line. If you don’t get the straight line, then you have to go back and check your calculations… x 1 2

12. Graphing
Use the ordered pair from the table to graph the linear equation.
Again…when graphing the result should be a straight line…
Any point (ordered pair) on that line will be a solution to the linear equation…

13. (x, y)
(0, - 1)
(1, 1)
(2, 3) x y
(2,3)
(1,1)
(0, -1)
y = 2x – 1

14. Your Turn
Find 3 different ordered pairs that are the solutions to the equation
y = 3x – 5
y = -2x – 6
y = ½ (4 – 2x)
y = 4( ½ x – 1)

15. More Comments…
Once you get the hang of it…this concept is really easy….
However, like everything else to become proficient you will need to practice…
It’s ok if you make a mistake…you can fix it…
The goal here is to keep an open mind and try…