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Graphing Linear Equations From the beginning All the slides in this presentation are timed. You do not need to click the mouse or press any keys on the keyboard for the presentation on each slide to continue. However, in order to make sure the presentation does not go too quickly, you will need to click the mouse or press a key on the keyboard to advance to the next slide. You will know when the slide is finished when you see a small icon in the bottom left corner of the slide. Click the mouse button to advance the slide when you see this icon. What is a Linear Equation? y A linear equation is an equation whose graph is a LINE. x Linear Not Linear What is a Linear Equation? y The equations we will be graphing have two variables, x and y. For example, 2x+ 3y = 12 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, 2(3)+ 3(2)= 12 If we were to plot all these ordered pairs on a graph, we would be graphing a line. x 2(0)+ 3(4)= 12 2(- 3)+ 3(6)= 12 2(6)+ 3(0)= 12 2(- 1)+ 3 4 2 = 12 3 ( ) Graphing a Linear Equation y How do we graph linear equations? Let’s try this one: y = 3x – 2 Make a Table of values x x y –2 –8 –1 0 –5 –2 1 1 2 4 yComplete = 3(–2) –the 2 = –8 by inputting ytable = 3(–1) – 2 = –5 the x - values and y = 3(0) – 2 = –2 calculating the y = 3(1) – 2 =y1corresponding values. y = 3(2) – 2 = 4 The x - values are picked by YOU! Graphing a Linear Equation y How about another one! Let’s try x – 2y = 5. First Step: Write y as a function of x x – 2y = 5 –2y = 5 – x y 5 1 x 2 2 x Graphing a Linear Equation y How about another one! Let’s try x – 2y = 5. Second Step: Make a Table of Values 5 1 x y y x 2 2 7 –2 Take a 2 moment –1 –3 and 0 5 complete 2 the chart… 1 –2 Click the screen when finished x Graphing Horizontal & Vertical Lines y 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 … x Graph x = 3 Since there are no y – values in this equation, x is always 3 and y can be any other real number. y = –2 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