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**Graphing Linear Equations**

From the beginning

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**What is a Linear Equation?**

y x A linear equation is an equation whose graph is a LINE. Not Linear Linear

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**What is a Linear Equation?**

y x The equations we will be graphing have two variables, x and y. For example, A solution to the equation is any ordered pair (x, y) that makes the equation true. The ordered pair (3 , 2) is a solution since, If we were to plot all these ordered pairs on a graph, we would be graphing a line.

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**Graphing a Linear Equation**

y x How do we graph linear equations? Let’s try this one: y = 3x – 2 Make a Table of values y = 3(–2) – 2 y = –8 x y –2 –1 1 2 The x - values are picked by YOU! –8 y = 3(–1) – 2 y = –5 Complete the table by inputting the x - values and calculating the corresponding y - values. –5 –2 y = 3(0) – 2 y= –2 1 4 y = 3(1) – 2 y= 1 y = 3(2) – 2 y= 4

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**Graphing a Linear Equation**

y x How about another one! Let’s try y = 5-2x. First Step: Make a Table of Values x y –2 –1 1 2 9 Take a moment and complete the chart… 8 5 3 1

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**Graphing Horizontal & Vertical Lines**

y x When you are asked to graph a line, and there is only ONE variable in the equation, the line will either be vertical or horizontal. For example … Graph x = 3 y = –2 Since there are no y – values in this equation, x is always 3 and y can be any other real number. Graph y = –2 Since there are no x – values in this equation, y is always – 2 and x can be any other real number. x = 3

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