5 5 Standard Form of a Linear Equation

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 1. Get the variables on the left and the constant on the right! 2. You must have the leading coefficient as a positive integer 3. You must have all numbers A, B and C as integers (whole numbers)

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

Practice: y=¾x+2 n (4)y = (4)¾ x + (4)2 Get rid of fractions. n 4 y = 3 x + 8 n -3 x Move all variables to the left. n -3 x + 4 y = 8 Make first coefficent positive. n (-1)(-3 x) + (-1)(4)y = (-1)(8) n 3 x – 4 y = -8 n

What about decimals? n n n n y = -0. 24 x - 5. 2 Multiply through by 100 to clear decimals, then put in standard form. (100)y = (100)(-0. 24) – (100)(5. 2) 100 y = -24 x – 520 24 x + 100 y = -520 (Now reduce if possible. ) 24 x + 100 y = -520 4 4 4 6 x + 25 y = -130

Real-life example: n n 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

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

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

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