1. 5.5 Standard Form of a Linear Equation

2. 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. 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)

4. 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.

5. 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

6. 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

7. 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

8. .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?

9. 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

10. 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