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5.5 Standard Form of a Linear Equation
Standard or General Form:
Ax + By = C
Where A, B and C are numbersx and y are the variables
A and B are called coefficients
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)
3 Rules for Standard Form
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. 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
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?
x-intercept (12, 0) and y-intercept (0, 18)
The graph will be in the first quadrant only.
Find the x and y intercepts.
12 Bananas
Ap
ple
s
18
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