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).

5.6 – Standard Form of a Linear Equation

QUESTION: How do we define an integer?

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!

x + 2y = 10

14x – 4y = 42

x + 5y = -70

5x + 2y = 15

NOT examples of linear equations in

standard form

x + y = 5

2x – 4y = 6

y = -1x -14

5x -15 = -2y

2

7

5

•x & y together

•an integer alone

•all integers, no fractions

•easy to find intercepts

•used in comparing 2 different types of things

NOT examples of linear equations in

standard form

•slope – intercept form y = mx + b

•point-slope formy – y1 = m(x – x1)

•any fractions present

Example: Write in standard form with integer coefficients.

35

2 xy Original Equation

)35

2(55 xy Get rid of the fraction

105 15

5y x Distribute

1525 xy Simplify

1552 yx Subtract 2x from each side

Done!

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.

Problem with Words in It

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.

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

Homework

Complete worksheet!