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Graphing Linear Equations Chapter 7.2

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Graphing an equation using 3 points 1. Make a table for x and y to find 3 ordered pairs. 2. I choose 3 integers for either x or y or any combination. 3. Substitute each value into the equation to solve for the other coordinate. (It’s easier to plot points with integers) 4. Plot the three points. 5. Draw a straight line through them.

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2 -1 -1 0 1 1. Make a table and graph the following: y = - 3x – 1 x = - 1 y = - 3( - 1) – 1 y = 3 – 1 y = 2 x = 0 y = - 3(0) – 1 y = 0 + - 1 y = - 1 x = 1 y = - 3(1) – 1 y = - 3 + ( - 1) y = - 4 -4-4 1. Make a table. 2. Choose integers for x. 3. Substitute and solve.

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2 -1 -1 0 1 -4-4 1. Make a table and graph the following: y = - 3x – 1 4. Plot each point. 5. Draw the line.

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4 3 -2-2 0 2 1extra. Make a table and graph the following: x + 2y = 6 x = - 2 - 2 + 2y = 6 x = 0 0 + 2y = 6 x = 2 2 + 2y = 6 2 1. Make a table. 2. Choose integers for x. 3. Substitute and solve. 2y = 8 y = 4 +2 +2 2 2 2y = 4 y = 2 -2 -2 2 2 2y = 6 y = 3 2 2

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4 3 -2-2 0 2 2 4. Plot each point. 5. Draw the line. 1extra. Make a table and graph the following: x + 2y = 6

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Graphing an equation 1. You may first take the given equation and solve for y. Then perform the other steps to graph.

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2. Make a table and graph the following: 7x + 3 = - 2y + 3 7x + 3 = - 2y + 3 1. Solve for y. 7x = - 2y y = -3 - 2 - 2 -7 2 x Now follow the 5 steps to graph this equation. = y -7 2 x

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2 ( - 2) -7 2 (2) 7 0 -2-2 0 2 2. Make a table and graph the following: x = - 2 x = 0 x = 2 -7-7 1. Make a table. 2. Choose integers for x. 3. Substitute and solve. y = 7 y = - 7 y = 0 y = -7 2 x y = y = 2 (0) y = -1 1

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7 0 -2-2 0 2 -7-7 4. Plot each point. 5. Draw the line. 2. Make a table and graph the following: y = -7 2 x

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Graphing an equation by its intercepts 1. Follow the same steps as before except when choosing the integers. 2. Let x = 0 and find the y-intercept. 3. Let y = 0 and find the x-intercept. 4. Find one more ordered pair.

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3 -6-6 0 0 2 3. Use the intercepts to graph the following: 2y – x = 6 x = 0 2y – 0 = 6 y = 0 2(0) – x = 6 x = 2 2y – 2 = 6 4 1. Make a table. 2. Choose x = 0 and y = 0. 3. Substitute and solve to find the intercepts. 2y = 6 y = 3 2 2 2y = 8 y = 4 +2 +2 2 2 -x = 6 x = - 6 -1 -1 4. Choose another value, I chose x = 2.

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3 0 0 -6-6 2 4 5. Plot each point. 6. Draw the line. 3. Use the intercepts to graph the following: 2y – x = 6

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Graphing horizontal and vertical lines 1. Some equations will have just one variable. 2. You may have to solve for that one variable. 3. If the equation has only the x, the line will be vertical passing through the x value on the x-axis. 4. If the equation has only the y, the line will be horizontal passing through the y value on the y-axis.

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4. Graph y = 2 The line is horizontal, passing through y = 2 on the y-axis.

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5. Graph 3x + 1 = - 8 Solve for x. The line is vertical, passing through x = - 3 on the x-axis. 3x + 1 = - 8 3x = - 9 x = - 3 -1 -1 3 3

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Graphing Linear Equations Chapter 7.2

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