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**LESSON 2.04: Graphing Linear Relations using a Table of Values MFM1P**

Graphing Linear Equations

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**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

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**Graphing Linear Equations**

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Leering Goals Students will graph linear equations using a table.

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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!

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**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.

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**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

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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…

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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…

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**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

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**? 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

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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…

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

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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)

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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…

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