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 6.4 Standard Form 6.4 NOTES
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Notes #27
HW #28
STANDARD FORM
Today you will learn how to write an equation in standard form given 1. a point on a line and the slope of the line or
2. two points on the line
6.4 Standard Form #27
6.2 Slope­ Intercept Form
Slope Formula
Point-Slope Form
Slope-Intercept Form
Standard Form
Ax + By = C
No Fractions
allowed
x­term can't
be negative
1. Find the slope between the points (1,3) and (­3,­5)
2. Find the point­slope form of the line passing
through the points (1,3) and (­3,­5)
(1,3)
(­3,­5)
6.4 Standard Form Write an equation of the line having the given slope and passing through the given point in the three formats:
A. Point­Slope Form y­y1 = m( x­ x1)
B. Slope­Intercept Form
C. Standard Form y = mx + b
Ax + By = C
4. m= 1 , (­8,6) 4
3. m=3, (4,2) a)
a)
b)
b)
c)
c)
x term can't be
negative
x term cannot be negative
Can't have fractions
x term can't be negative
Can't have fractions so multiply through by the common denominator
6.4 Standard Form Write an equation of the line having the given slope and passing through the given point in the three formats:
y­y1 = m( x­ x1)
A. Point­Slope Form B. Slope­Intercept Form y = mx + b
Ax + By = C
C. Standard Form 5. (­3,0), (6,­6)
x term cannot be negative
Can't have fractions
6. (­7,­6), (­5,­3)
Slope
6 2
­
m= 0+6
= = ­3­6 ­9
3
m
e for
p
o
l
s
­
pt
a)
(­3,0) y­0 =­ 23 (x+3)
b) (­3,0) y­0 = (x+3)
a)
b)
ept terc
n
i
­
e
p
o
sl
form c)
c)
fo
standard
rm Can't have fractions so multiply through by the common denominator
x term can't be negative
Can't have fractions so multiply through by the common denominator
6.4 Standard Form Write an equation of the line having the given slope and
passing through the given point in the three formats:
A. Point­Slope Form r e
w
s
n
A
B. Slope­Intercept Form
!
e
n
o
s
i
h
t
y
C. Standard Form !
r
e
g
a
p
You t
xt
e
n
e
h
(0,6) (­4,3)
is on t
a) slope
b) point­slope form
c) slope­intercept form
[choose only one of the points to find the slope­intercept form equation.] [write both equations]
d) standard form
[use the slope­intercept equation to write the equation in standard form.] 6.4 Standard Form Write an equation of the line having the given slope and passing through the given
point in the three formats: A. Point­Slope Form B. Slope­Intercept Form
C. Standard Form (0,6) (­4,3)
b) point­slope form
a) slope
[write both equations]
c) slope­intercept form [choose only one of the points to find the slope­intercept form equation.] Note: it does not matter which equation you choose to solve because both point­slope equations will end with the same slope­intercept answer
d) standard form
OPTION 1
[use the slope­intercept equation to write the equation in standard form.] OPTION 1:
1. Move x­term left
2. Rearrange terms on
left
3. If x­term is negative,
change the signs on
entire equation.
4. If there are any
fractions, multiply
through by the
common denominator
OPTION 2:
1. If there are any
fractions, multiply
through by the
common denominator
2. Move x­term left
3. Rearrange terms on
left
4. If x­term is negative,
change the signs on
entire equation.
OPTION 2
Remember:
First term (x­term) can't be negative
No fractions allowed!
You choose the option you would prefer to use!