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The equation 2 3y x is written _______________ form.
If we move “ 2xwe have _______________________.
” to the other side of the equation,
2 3y x slope intercept
2x
2 3x y
2 3x y
If we move “ 2xwe have _______________________.
” to the other side of the equation,
2 3x y
This is still a ________ equation, but it is written in a different form.
linear
A linear equation in the form _______________ is in ______________, where A, B, and C are integers.
Ax By C standard form
A linear equation in the form _______________ is in ______________, where A, B, and C are integers.
Ax By C standard form
Remember the set of integers is
.... 4, 3, 2, 1, 0,1, 2, 3, 4...
NO FRACTIONS!!!NO DECIMALS !!!
Example 1:A. Jackie is in charge of selling tickets for the school jazz
concert at $2.00 for students and $4.00 for adults. She hopes that the total ticket sales will be about $600 in order to cover expenses and make a modest profit. Write a linear equation in standard form to model this
situation.
Let x y
# student tickets
# adult tickets
$2.00
$4.00
2.00 4.00 600x y
2 4 600x y
B. A donation of $300 was make to the Classical Music Club for the purpose of building their collection of CDs. At the local music store, some classical CDs cost $10 and other cost $15. The club wants to know how many of each type can buy with the $300.
(Do not consider sales tax.) Write an equation in standard form to model this
situation.Let x
y
# classical CDs
# other CDs
$10.00
$15.00
10.00 15.00 300x y
10 15 300x y
5 2 4y x
x-term + y-term = constantNo fractions, no decimals ! 4 2 2x y
5 8
7y x
2 5
3x y
7 3 5x y
7.5 4.3x y
A
B
C
D
E
F
Example 2: Tell whether the equations below are in standard form.
NO
YES
NO
NO
YES
NO
FRACTIONS
DECIMALS
If an equation is not written in standard form, we can rewrite the equation so that it is in standard form.
Example 3: Write each linear equation in standard form.
A. 57 2 4y x B. 3 8
7y x 2y
57 4 2x y
4 2 57x y
7 7 7
7 3 56y x 3x
3 7 56x y
3 7 56x y 4 2 57x y
C. 57 2 4y x D.
53
57 40 53x y
57 4 2x y
2y
4 2 57x y
4 2 57x y 57 40 53x y
5.7 5.3 4x y 10 10 10
57 53 40x y 40y
We can find the ___& ___ intercepts and the ________ when the equation is written in standard form.
x y slope
x-intercept is at
y
y-intercept is at
x ( 2,0)
0
(0,3)
0
x-intercept is at
y
y-intercept is at
x ( 2,0)
0
(0,3)
0
We know that y = 0 at the ____ intercept, so we can plug in 0 for ___ to find the _____ intercept.
We know that x = 0 at the ____ intercept, so we can plug in 0 for ___ to find the _____ intercept.
xy x
yyx
Example 4: Find the x & y intercepts of the following equations.
A. 4 2 12x y
x- intercept y-intercept
Plug in 0 for y
Plug in 0 for x
0 4 2 12x
4 12x 4 4
3x
intercept 3,0x
4 10 2 2y
2 12y 2 2
6y
intercept 0, 6y
Example 4: Find the x & y intercepts of the following equations.
B.
x- intercept y-intercept
Plug in 0 for y
Plug in 0 for x
2 3 180x
2 18x 2 2
9x
intercept 9,0x
2 3 10 8y
3 18y 3 3
6y
intercept 0, 6y
2 3 18x y
Example 4: Find the x & y intercepts of the following equations.
C.
x- intercept y-intercept
Plug in 0 for y
Plug in 0 for x
0 Ax B C
Ax C A A
C
xA
intercept ,0C
xA
0A By C By C
B B
C
yB
intercept 0,C
yB
Ax By C
x- intercept y-intercept
C
xA
intercept ,0C
xA
C
yB
intercept 0,C
yB
Ax By C
Write in slope-intercept form to find the slope. Ax By C
Ax By C Ax
By Ax C B B B
A C
y xB B
x- intercept y-intercept
C
xA
intercept ,0C
xA
C
yB
intercept 0,C
yB
Ax By C
A
mB
x - intercept =
y - intercept = Slope =
C
A
Ax CBy
To find the x-intercept, cross out the y-term…
B
A
x - intercept =
y - intercept = Slope =
C
A
Ax CBy
B
A
To find the y-intercept, cross out the x-term…
C
B
-3 2 12x y
Example 5: Find the slope and x & y intercepts of the following equations.
A.
A =
B =
C =
3
2
12Slope x- intercept y-intercept
Am
B
3
2m
3
2m
Example 5: Find the slope and x & y intercepts of the following equations.
A. -3 2 12x y A =
B =
C =
3
2
12Slope x- intercept y-intercept
Am
B
- int
Cx
A
3
2m
3
2m
3- int
12x
- int 4x
Example 5: Find the slope and x & y intercepts of the following equations.
A. -3 2 12x y A =
B =
C =
3
2
12Slope x- intercept y-intercept
Am
B
- int
Cx
A -int
Cy
B
3
2m
3
2m
3- int
12x
- int 4x
- int12
2y
- int 6y
Example 5: Find the slope and x & y intercepts of the following equations.
A. -3 2 12x y A =
B =
C =
3
2
12Slope x- intercept y-intercept
Am
B
- int
Cx
A -int
Cy
B
3
2m
3
2m
3- int
12x
- int 4x
- int12
2y
- int 6y
Example 5: Find the slope and x & y intercepts of the following equations.
B.
A =
B =
C =
5
3
30Slope x- intercept y-intercept
Am
B
5
3m
5
3m
5 3 30x y
Example 5: Find the slope and x & y intercepts of the following equations.
B.
A =
B =
C =
5
3
30Slope x- intercept y-intercept
Am
B
5
3m
5
3m
5 3 30x y
- intC
xA
- int30
5x
- int 6x
Example 5: Find the slope and x & y intercepts of the following equations.
B.
A =
B =
C =
5
3
30Slope x- intercept y-intercept
Am
B
5
3m
5
3m
5 3 30x y
- intC
xA
- int30
5x
- int 6x
-intC
yB
3- int
30y
- int 10y
Example 5: Find the slope and x & y intercepts of the following equations.
B.
A =
B =
C =
5
3
30Slope x- intercept y-intercept
Am
B
5
3m
5
3m
5 3 30x y
- intC
xA
- int30
5x
- int 6x
-intC
yB
3- int
30y
- int 10y
4 6 12x y
Example 5: Find the slope and x & y intercepts of the following equations.
C.
A =
B =
C =
4
6
12Slope x- intercept y-intercept
Am
B
4
6m
2
3m
4 6 12x y
Example 5: Find the slope and x & y intercepts of the following equations.
C.
A =
B =
C =
4
6
12Slope x- intercept y-intercept
Am
B
4
6m
2
3m
- intC
xA
2- int
1
4x
- int 3x
4 6 12x y
Example 5: Find the slope and x & y intercepts of the following equations.
C.
A =
B =
C =
4
6
12Slope x- intercept y-intercept
Am
B
4
6m
2
3m
- intC
xA
2- int
1
4x
- int 3x
-intC
yB
2- int
1
6y
- int 2y
4 6 12x y
Example 5: Find the slope and x & y intercepts of the following equations.
C.
A =
B =
C =
4
6
12Slope x- intercept y-intercept
Am
B
4
6m
2
3m
- intC
xA
2- int
1
4x
- int 3x
-intC
yB
2- int
1
6y
- int 2y
If an equation is written in standard form, you can use the _______________ to graph the equation quickly.
Ax By C
x & y intercepts