Lesson 5-5
Standard Form
Sept. 24, 2014
Daily Learning Target
• I will write and graph equations in standard
form.
Intercepts
• Think about what the word “intercept”
means.
• What does the
y-intercept look like?
• What does the
x-intercept look like?
Standard Form
• Any linear equation can be expressed in the form
Ax + By = C where A, B, and C are integers and A
and B are not both zero. This is called standard
form. An equation that is written in point-slope
form can be written in standard form.
• Rules for Standard Form:
• Standard form is Ax + By = C, with the following
conditions:
1) No fractions
2) A is not negative (it can be zero, but it can't be
negative).
By the way, "integer" means no fractions, no
decimals. Just clean whole numbers (or their
negatives).
Example 1
• Find the x- and y-intercepts of the graph of
3x + 4y = 24
We will substitute 0 for the x and y (at different
times) to identify the intercepts.
x-int. = 8
x=8
and
y-int. = 6
y=6
You Try
• What are the x- and y-intercepts of the graph
of each equation.
1) 5x – 6y = 60
x = 12; y = -10
2) 3x + 8y = 12
x = 4; y =
3
2
Example 2
• What is the graph
of x – 2y = -2
• Find the x- and yintercepts.
x = -2; y = 1
• Graph each
intercept and
connect the points
You Try
• What is the graph
of 2x + 5y = 10?
Graphing Horizontal and Vertical Lines
• What is the graph
of each equation?
1) x = 3
2) y = 3
You Try
• What is the graph
of each equation?
1) x = 2
2) y = -5
Transforming to Standard Form
• What is y = -
3
x
7
+ 5 written in standard form?
• Step 1: Get rid of the fraction (distributive
property)
• Step 2: Get the x and y on the same side of
the equal sign.
Transforming to Standard Form
• Write y – 2 = -
1
(x
3
+ 6)
• Step 1: Simplify to get rid of the parenthesis
• Step 2: Get rid of the fraction
• Step 3: Rearrange the equation to put x and y
on the same side.
Model
• The iTunes store sells songs for $1 each and
movies for $12 each. You have $60 to spend.
Write and graph an equation that describes
the items you can purchase. What are three
combinations of numbers of songs and movies
you can purchase?
You Try
• In the last example, suppose the store
changed the price of movies to $15 each.
What equation describes the number of songs
and movies you can purchase for $60.
• What domain and range are reasonable for
the above equation? Explain.
Homework
• Workbook
• Page 155 problems 3, 5, 6, 8, 9, 10-12, 17, 20
• Page 157 problems 1-5