Download x-intercept

Standard Form
2015-2016
Objective: To be able describe
Warm-Up:
What are intercepts?

Where your graph crosses your x and y-axis
Intercepts:
x-intercept:
The x-coordinate of the point where the graph intersects the x-axis.
The y-coordinate of this point is always 0.
y-intercept:
The y-coordinate of the point where the graph intersects the x-axis.
The x-coordinate of this point is always 0.
How do we find intercepts?
To find the x-intercept we….
Replace zero for y, and solve the
equation for x
Example: 3x-2y = 12
How do we find intercepts?
To find the y-intercept we….
Replace zero for x, and solve the
equation for y
Example: 3x-2y = 12
Let’s try another example:
Find the x and y intercepts of the equation:
−3𝑥 + 5𝑦 = 30
How do we find intercepts given a graph?
Look to see where
your graph crosses
the _________ and
the __________
X-int = (
Y-int = (
, )
, )
You Try:

Find the x and y- intercept of the graph:
Standard Form:
𝐴𝑥 + 𝐵𝑦 = 𝐶
where A is a whole number, and
B, and C are integers.
(A & B can NOT both be 0)
Identify if the following are in standard form:
Recall: Standard Form is 𝐴𝑥 + 𝐵𝑦 = 𝐶

𝑦 = 3𝑥 + 5

𝑦=
1
𝑥
3

3𝑥 − 2𝑦 = 8

−2𝑦 + 3𝑥 = 5
Quiz Yourself: Are the following equations (As SEEN) in standard form.
A
B
C
D
5 y  2  4x
4 x  2 y  2
5
y   x 8
7
2
x  y  5
3
NO
YES
𝐴𝑥 + 𝐵𝑦 = 𝐶
x-term + y-term = constant
No fractions, no decimals !
NO
NO
E
 7 x  3 y  5
NO
F
7.5x  y  4.3
NO
FRACTIONS
NEGATIVE A
VALUE
DECIMALS
Rewrite the following equations in standard form:
A.
57  2 y  4 x
2 y 2 y
57  4 x  2 y
B.
3
7
7 y   x  87
7
7y  3 x  56
3x 3x
3 x  7 y  56
4 x  2 y  57
3 x  7 y  56
Recall: Standard Form is 𝐴𝑥 + 𝐵𝑦 = 𝐶
Rewrite the following equations in standard form:
C.
10
10
10
5.7 x  5.3  4 y
57 x  53  40 y
57𝑥 − 40𝑦 = 53
D. −1 −2𝑥 + 4𝑦 =−1 8
2𝑥 − 4𝑦 = −8
2𝑥 − 4𝑦 = −8
Recall: Standard Form is 𝐴𝑥 + 𝐵𝑦 = 𝐶
How to graph using standard form:
Graph:
2𝑥 + 3𝑦 = 12
Step 1: Find the x and y
intercept and express as an
ordered pair.
x-Intercept:
Plug _____ in for ______
y-Intercept:
Plug _____ in for ______
Step 2: Plot your 2 intercepts, and graph (connect the
dots)
You try!

Graph:
5𝑥 + 2𝑦 = −10
Write an equation in standard form:
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.
Let
x
y
# student tickets
$2.00
# adult tickets
$4.00
2.00 x  4.00 y  600
2 x  4 y  600
Find the intercepts, and explain what they represent?
Write an equation in standard form to model example 2 below:
A donation of $300 was made 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 they buy with the $300. (Do
not consider sales tax.)
Let
x
y
# classical CDs
$10.00
# other CDs
$15.00
10.00 x  15.00 y  300
10 x  15 y  300
Find the intercepts, and explain what they represent?