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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!