Download standard form

STANDARD FORM
OF A LINEAR EQUATION
Students will be able to graph linear
equations using intercepts and write
linear equations in standard form.
The equation y  2 x  3
is written _______________
form.
slope intercept
y  2 x  3
2x
2x  y  3
If we move “
 2x ” to the other side of the equation,
2x  y  3
we have _______________________.
If we move “
 2x ” to the other side of the equation,
2x  y  3
we have _______________________.
linear
This is still a ________
equation, but it is written
in a different form.
Ax  By  C
A linear equation in the form _______________
standard form where A, B, and C are
is in ______________,
integers.
Ax  By  C
A linear equation in the form _______________
standard form where A, B, and C are
is in ______________,
integers.
Remember the set of integers is



...  4, 3, 2, 1, 0, 1, 2, 3, 4...
.
NO FRACTIONS!!!
NO DECIMALS !!!



Tell whether the equations below are in standard form.
A
5 y  2  4x
NO
4 x  2 y  2
YES
5
y   x8
7
2
x  y  5
3
NO
E
 7 x  3 y  5
YES
F
7.5x  y  4.3
NO
B
C
D
NO
x-term + y-term = constant
No fractions, no decimals !
FRACTIONS
DECIMALS
If an equation is not written in standard form, we can
rewrite the equation so that it is in standard form.
Write each linear equation in standard form.
A.
57  2 y  4 x
2 y
B.
7y   3 7x  8 7
7
57  4 x  2 y
4 x  2 y  57
7y  3x  56
3x
3 x  7 y  56
4 x  2 y  57
3 x  7 y  56


Convert this equation into
standard form: Ax + By = C
2
y  x 3
5
Multiply everything by 5

5y  2x 15
-2x
Move over the “x” term
-2x
2x  5y  15
2x  5y  15
IT CAN’T LEAD WITH A NEGATIVE!!!
So let’s change the sign of each term.
It’s kind of like
moving backwards!
Convert this equation into
standard form: Ax + By = C
y  x  5
+x
+x

xy 5

Move over the “x” term
Convert this equation into
standard form: Ax + By = C
1
y
x7
2
Multiply everything by 2
2y  1x 14
Move over the “x” term

+ 1x


+ 1x
x  2y  14
Convert this equation into
standard form: Ax + By = C
2
y  x4
3
Multiply everything by 3
3y  2x 12
Move over the “x” term

-2x


-2x
2x  3y  12
2x  3y  12
IT CAN’T LEAD WITH A NEGATIVE!!!
So let’s change the sign of each term.
Write an equation of the line in STANDARD
FORM using the information given.
m = 2 and (3,-2)
Start with slope-intercept form
y  2x  8
-2x

Now put into Standard form

No LEADING NEGATIVES!
Change all the signs of each term
-2x
2x  3y  12
2x  3y  12
Ax  By  C
If an equation is written in standard form, you can
x & y intercepts to graph the equation
use the _______________
quickly.
x ___
y intercepts and the ________
slope
We can find the ___&
when the equation is written in standard form.
y-intercept is at
x-intercept is at
( 2, 0)
y
0
(0, 3)
x
0
x-intercept
is at
( 2, 0)
y-intercept is
at
(0, 3)
x 0
y0
x intercept,
We know that y = 0 at the ____
y to find the _____
x intercept.
so we can plug in 0 for ___
We know that x = 0 at the ____
y intercept,
x to find the _____
y intercept.
so we can plug in 0 for ___
Example 4: Find the x & y intercepts of the following equations.
A.
4 x  2 y  12
Plug in
0 for y
x- intercept
y-intercept
4 x  2  0  12
4x  12
4
Plug in
0 for x
4
x  3
x intercept   3,0
4  0  2 y  12
2 y  12
2
2
y  6
y intercept   0, 6
Example 4: Find the x & y intercepts of the following equations.
B.
2 x  3 y  18
Plug in
0 for y
x- intercept
y-intercept
2 x  3  0  18
2x  18
2
Plug in
0 for x
2
x9
x intercept   9,0
2  0  3 y  18
3 y  18
3
3
y  6
y intercept   0, 6
Exit Card & Homework
Exit Card: Write the equation in Standard
Form (Ax + By = C)
y = -2x – 4
Homework: WB p. 155-156 #2-32 (EVEN)