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Published byDiana Walters Modified over 9 years ago

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Do Now 10/26/10 In your notebook, explain how you know a function is a function. Then answer if the following three tables are functions or not. x 02448 y43210 x11235 y43210 x12345 y336810 Each input must be paired with only ONE output Not a function Function

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Objective graph 7 linear equations and linear functions in a coordinate plane

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Section 4.2 “Graph Linear Equations” Linear Equation- an equation whose graph is a line The STANDARD or GENERAL FORM of a linear equation is represented as Ax + By = C where A, B, and C are real numbers

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Linear Equations An example of a linear equation in two variables is -3x + 2y = 5 the solution of an equation in two variables, x and y, is an ordered pair (x, y) that produces a true statement when substituted into the equation. Which ordered pair is a solution of -3x + 2y = 5? A. (3,4) B. (1,-1) C. (-1, 1) D. (0,-1)

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2 4 6 8 10 024681012 y-axis x-axis (-2,-10) -12-10-8-6-4-2 -10 -8 -6 -4 -2 Graph an Equation Graph the equation y = -4 + 3x. xy -2-10-7 (-1,-7) 0-4 (0,-4) 1 (1,-1) 22 (2,2)(2,2)(2,2)(2,2) y = -4 + 3x

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Graph an Equation Solve the equation for y. STEP 1 SOLUTION Graph the equation y + 2x = 4. STEP 2 Make a table by choosing a few values for x and then finding values for y. STEP 3 Plot the points. Notice the points appear on a line. Connect the points drawing a line through them. x-2012 y86420

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Graph an Equation Solve the equation for y. STEP 1 SOLUTION Graph the equation -2x + y = -3. STEP 2 Make a table by choosing a few values for x and then finding values for y. STEP 3 Plot the points. Notice the points appear on a line. Connect the points drawing a line through them. x-2012 y-7-5-31

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Graph an Equation Solve the equation for y. STEP 1 SOLUTION Graph the equation 0x + 1y = 2. STEP 2 Make a table by choosing a few values for x and then finding values for y. STEP 3 Plot the points. Notice the points appear on a line. Connect the points drawing a line through them. x-2012 y22222

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Graph an Equation Solve the equation for x. STEP 1 SOLUTION Graph the equation x = -1. STEP 2 Make a table by choosing a few values for x and then finding values for y. STEP 3 Plot the points. Notice the points appear on a line. Connect the points drawing a line through them. x y-2012

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Linear Function- The equation Ax + By = C represents a linear function as long as B = 0.

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Graph a Function SOLUTION12 Graph the function y = – x + 4 with domain x ≥ 0. Then identify the range of the function. STEP 1 Make a table. x 02468 y43210 STEP 2 STEP 3 Connect the points with a ray because the domain is restricted. Plot the points. STEP 4 Identify the range. From the graph, you can see that all points have a y - coordinate of 4 or less, so the range of the function is y ≤ 4.

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Graph a Function SOLUTION STEP 1 Make a table. STEP 2 STEP 3 Connect the points with a ray because the domain is restricted. Plot the points. STEP 4 Identify the range. From the graph, you can see that all points have a y-coordinate of 1 or more, so the range of the function is y ≥ 1. Graph the function y = – 3x + 1 with domain x ≤ 0. Then identify the range of the function. x 0– 1– 2– 3– 4 y1471013

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