Goal:

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 instandard
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 instandard
form
NOT ? examples of linear equations instandard
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.
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!