Transcript 5.6 The Standard Form of a Linear Equation - Link 308

Algebra 1
No trumpets sound
when the important
decisions of our life
are made. Destiny is
made known
silently.
Agnes DeMille
Today:
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•
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5.5 Assignment
5.5 Check Up
5.6 Instruction
Practice
Algebra 1
No trumpets sound
when the important
decisions of our life
are made. Destiny is
made known
silently.
Agnes DeMille
Assignment:
• 5.5 p303 #3-17 odd,
21-37, 48, 51-55 odd,
• Chapter 5 Test on
Monday
5.6
CHECK UP
Find the equations of the lines. Use slope-intercept form.
1. theline thatpasses through(5, 32)and(7,16)
y  8 x  72
2. theline thatpasses through(-12,- 15)and(-18,-12)
1
y   x  21
2
3. theline thatpasses through(2, - 5) and(2,-30)
x2
2
4. perpendicular to y  x - 2 andpasses through(8, 3)
3
3
y   x  15
2
5. A sports
a registration fee and a daily
y  24camp
x  50charges
$770
amount. If a total bill for 12 days is $338 and for 19 days
a bill is $506, find the equation that determines the
charges for this camp. How much would 30 days cost?
5.6
The Standard Form of a Linear
Equation
Objectives:
1. Write linear equations in standard form
2. Using standard forms of linear equations in the
real world
Vocabulary: standard form
5.6
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The Standard Form of a Linear
Equation
y = mx + b
Slope-Intercept form
– Used to graph a line
– Used to find equations of lines
Point-Slope form
y - y1=m(x - x1)
– Used to find equations of lines
Standard Form
Ax + By = C
– Used in Real World
– Used to graph a line (intercepts)
Example 1
Writing an Equation in Standard Form
Ax + By = C
To write an equation in standard form.
1. Eliminate fractions (multiply by denominators)
2. Move x & y terms to the left side and
constant (number) to the right side.
Write these linear equations in standard form:
y = 3x + 4 -3x + y = 4
2x + 3y + 4 = 5x – 4y – 5
y – 4 = 6(x – 2)
-3x + 7y = -9
6x – y = -8
Example 1
Writing an Equation in Standard Form
Ax + By = C
To write an equation in standard form.
1. Eliminate fractions (multiply by denominators)
2. Move x & y terms to the left side and
constant (number) to the right side.
Write these linear equations in standard form:
2
1
y x-2
 5x  11  y
2x
+
-3y
=
6
3
2
3
y  x 7
5
-3x + 5y = 35
10x + 11y = 22
Example 2
Finding Equations in Standard Form
Write the standard form of an equation of the line passing
through (-4,3) with a slope of -2.
2x + y = -5
Write the standard form of an equation of the
3
line passing through (-5,1) with a slope of 4 .
-3x + 4y = 19
Example 2
Finding Equations in Standard Form
Write the standard form of an equation of the line passing
through (3,0) and (-5,3).
3x + 8y = 9
Example 3
Horizontal and Vertical Lines
7
6
5
Write the equation of the
line shown in the graph in
standard form.
4
3
2
1
-6
y=4
x = -3
-4
-2
1 2 3 4 5 6 7
-2
-4
-6
y = -7
x=1
Example 4
Horizontal and Vertical Lines
Write the standard form of an equation of the horizontal
line passing through (5,7).
y=5
Write the standard form of an equation of the
vertical line passing through (3,-6).
x=3
Example 5
Standard Equations in Real Life
If you have $50 to spend at a used book sale. They
can buy paperbacks for $1 and hardcover books for
$4. Find a linear equation to model the possible
combinations of books.
x + 4y = 50
How many paperback
books you could buy?
50 paperbacks
How many hardcovers
books could you buy?
12 hardcovers
Example 5
Standard Equations in Real Life
You are in charge of purchasing apples and oranges
for the camp you work at during the summer. A bag
of oranges costs $4 and a bag of apples costs $3.00.
You have $48 dollars to spend. Write an equation
that models the possible ways you can buy bags of
oranges and apples.
4x + 3y = 48
Make a table of possible costs.
Oranges
Apples
Example 5
Standard Equations in Real Life
You are in charge of purchasing apples and oranges
for the camp you work at during the summer. A bag
of oranges costs $4 and a bag of apples costs $3.00.
You have $48 dollars to spend. Write an equation
that models the possible ways you can buy bags of
oranges and apples.
4x + 3y = 48
Make a table of possible costs.
Oranges
0
3
6
9
12
Apples
Example 5
Standard Equations in Real Life
You are in charge of purchasing apples and oranges
for the camp you work at during the summer. A bag
of oranges costs $4 and a bag of apples costs $3.00.
You have $48 dollars to spend. Write an equation
that models the possible ways you can buy bags of
oranges and apples.
4x + 3y = 48
Make a table of possible costs.
Oranges
0
3
Apples
16
12
6
9
12
8
4
0
5.6
Assignment:
5.6 p311 #5-15 odd, 16, …
To write an equation in standard form.
1. Eliminate fractions (multiply by
denominators)
2. Move x & y terms to the left side and
constant (number) to the right side.
Algebra 1
No trumpets sound
when the important
decisions of our life
are made. Destiny is
made known
silently.
Agnes DeMille
Assignment:
• 5.6 p311 #3-15 odd,
16,18-60 x3, 64, 67-69
• Chapter 5 Notes Quiz
on Monday
• Chapter 5 Test on
Tuesday