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5.5 Standard Form of a Linear Equation

5.5 Standard Form of a Linear Equation. 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. Standard or General Form:. Ax + By = C

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5.5 Standard Form of a Linear Equation

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  1. 5.5 Standard Form of a Linear Equation

  2. 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.

  3. 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

  4. 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)

  5. 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.

  6. Practice: • y = ¾ x + 2 • (4)y = (4)¾ x + (4)2 Get rid of fractions. • 4y = 3x + 8 • -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

  7. 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 = -520 (Now reduce if possible.) • 24x + 100y = -520 4 4 4 • 6x + 25y = -130

  8. 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

  9. .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?

  10. 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 18 12 Bananas

  11. 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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