1. 5.6 – Standard Form of a Linear Equation
Goal:
- Write a linear equation in standard form
- Use the standard form of an equation to model a real life situation (that means a word problem).
QUESTION: How do we define an integer?

2. You will USUALLY have to transform FROM slope intercept or point slope form TO Standard Form.
That just means that you will have to add or subtract to get the variables on the LEFT, the constant on the RIGHT.
Be careful if you have coefficients or the constant term is NOT an integer. You WILL have to get rid of the fraction (but not necessarily by multiplying by the reciprocal!

3. YES  examples of linear equations in standard form
NOT  examples of linear equations in standard form
x + y = 5
2x – 4y = 6
y = -1x -14
5x -15 = -2y
x + 2y = 10
14x – 4y = 42
x + 5y = -70
5x + 2y = 15 2 7 5

4. YES  Examples of linear equations in standard form
NOT  examples of linear equations in standard form
x & y together
an integer alone
all integers, no fractions
easy to find intercepts
used in comparing 2 different types of things
slope – intercept form
y = mx + b
point-slope form
y – y1 = m(x – x1)
any fractions present

5. Example: Write in standard form with integer coefficients.
Original Equation
Get rid of the fraction
Distribute
Simplify
Subtract 2x from each side
Done!

6. Problem with Words in It
You are in charge of buying the hamburger and boned chicken for a BBQ. The hamburger costs $2 per pound and the boned chicken costs $3 per pound. You have $30 to spend.
a. Write an equation that models the different amounts of hamburger and chicken that you can buy.
b. Make a table and a graph that illustrate several different amounts of hamburger and chicken that you can buy.

7. Equations of Lines
Slope Intercept Form: y = mx + b
Point-Slope Form: y – y1 = m(x – x1)
Vertical Line (undefined slope): x = x-intercept
Horizontal Line (Zero Slope): y = y-intercept
Standard Form (Define A, B, C): Ax + By = C

8. Homework
Complete worksheet!