5.5 Standard Form of a Linear Equation

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

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)

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.

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

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

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

.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?

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

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