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**5.5 Standard Form of a Linear Equation**

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Learning Goal #1 for Focus 4 (HS.A-CED.A.2, HS.REI.ID.10 & 12, HS.F-IF.B.6, HS.F-IF.C.7, HS.F-LE.A.2): The student will understand that linear relationships can be described using multiple representations. 4 3 2 1 In addition to level 3.0 and above and beyond what was taught in class, the student may: · Make connection with other concepts in math · Make connection with other content areas. The student will understand that linear relationships can be described using multiple representations. - Represent and solve equations and inequalities graphically. - Write equations in slope-intercept form, point-slope form, and standard form. - Graph linear equations and inequalities in two variables. - Find x- and y-intercepts. The student will be able to: - Calculate slope. - Determine if a point is a solution to an equation. - Graph an equation using a table and slope-intercept form. With help from the teacher, the student has partial success with calculating slope, writing an equation in slope-intercept form, and graphing an equation. Even with help, the student has no success understanding the concept of a linear relationships.

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**Standard or General Form:**

Ax + By = C Where A, B and C are numbers x and y are the variables A and B are called coefficients

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**3 Rules for Standard Form**

Get the variables on the left and the constant on the right! You must have the leading coefficient as a positive integer You must have all numbers A, B and C as integers (whole numbers)

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**How to change from slope-intercept form to Standard form**

Step 1: Clear out any fractions or decimals by multiplying all numbers by the denominator or by the place value of the decimal. Step 2: Move the x and y variable to the left side. Keep the constant on the right side. Step 3: Make sure the x coefficient is positive. If not, multiply all terms by -1.

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**Practice: y = ¾ x + 2 (4)y = (4)¾ x + (4)2 Get rid of fractions.**

-3x -3x Move all variables to the left. -3x + 4y = 8 Make first coefficent positive. (-1)(-3x) + (-1)(4)y = (-1)(8) 3x – 4y = -8

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**What about decimals? y = -0.24x - 5.2**

Multiply through by 100 to clear decimals, then put in standard form. (100)y = (100)(-0.24) – (100)(5.2) 100y = -24x – 520 24x + 100y = (Now reduce if possible.) 24x + 100y = 6x + 25y = -130

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Real-life example: You have $6.00 to use to buy apples and bananas. If bananas cost $.49 per pound, and apples cost $.34 per pound, write an equation that represents the different amounts of each fruit you can buy. Graph it. Let x = bananas and y = apples

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.49x + .34y = 6 Since we are using standard form, we will multiply through by 100 to clear out decimals. Therefore: 49x + 34y = 600 What do we do now to graph this?

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**Find the x and y intercepts.**

x-intercept (12, 0) and y-intercept (0, 18) The graph will be in the first quadrant only. Apples Bananas

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Practice: Put in standard form the line passing through point (2, -3) with a slope of 3. 3x – y = 9 Put in standard for the horizontal line going through point (-2, 6) y = 6

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