Download Name: Date: Period: ____ Most of the linear equations that we have

Name: ____________________________
Date: _________________
Period: ____
Objectives: To transform a linear equation into standard form
To model a real-life situation using the standard form of a linear equation
Most of the linear equations that we have worked with so far have been written in slope-intercept form.
y = mx + b
Slope-Intercept Form
Another commonly used form for linear equations is standard form.
Ax + By = C Standard Form
Notice that in standard form the ‘x’ and ‘y’ variables are on the left side of the equation and the constant
term is on the right side.
‘OH MY
I JUST LOVE
Rules for Standard Form:
STANDARD
 No Fractions
FORM OF A
 The ‘x’ term must be positive
LINE …’
 ‘x’ and ‘y’ must be on the same side
(usually the left side)
 The constant term must be all alone
(usually the right side)
Transforming a Linear Equation into Standard Form
Example 1
Transform y 
2
x  3 into standard form.
5
2
y  x 3
original equation
5
5y = 2x – 15
-2x + 5y = -15
2x – 5y = 15
So the linear equation y 
multiply both sides by 5
subtract 2x from both sides
multiply/divide everything through by -1
2
x  3 written in standard form is 2x – 5y = 15.
5
Try these!!!
Write the following equations in standard form.
1. 3x – y – 6 = 0
2. 2x – 12 = 3y
3. y = -3x + 4
___________
____________
___________
Modeling Standard Form of an Equation in Real-Life Situations
Example 2
Picture It… You have $10 to buy tomatoes and avocados for a salad. Tomatoes cost $1.25 per pound and
avocados cost $2 per pound. Write a linear equation that represents the different amounts of tomatoes,
x, and avocados, y, that you could buy.
Now use your linear equation to fill in the table below:
Tomatoes, x
0 lb
1.6 lb
4 lb
6.4 lb
8 lb
Avocados, y
Try This!!!
4. You are running for class president. You have $30 to spend on publicity. It costs $2 to make a
campaign button and $1 to make a poster. Write an equation that represents the different numbers
of buttons, x, and posters, y, you could make.
Use your linear equation to answer the following questions:
(a) How many buttons can you make if you make 6 posters?
________
(b) How many posters can you make if you make 8 buttons?
________
Let’s pull together everything we have learned thus far in this unit…
Write an equation of a line, in standard form, that passes through the given point and has the given slope.
5. (-4, 3) m = -1
6. (0, 5) m = 2
7. (-4, -2) m = ½
____________
____________
_____________
Write an equation of a line, in standard form, that passes through the two given points.
8. (-2, -1) (2, -3)
9. (2, 4) (8, 6)
10. (8, 3) (9, -4)
___________
____________
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