point – slope & slope – intercept forms point – slope - uses a slope ( m ) and a point (...
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Point – Slope & Slope – Intercept Forms
Point – Slope - uses a slope ( m ) and a point ( a , b ) to
define a line
y = m ( x – a ) + b
Slope – Intercept – uses a slope ( m ) and a y – intercept ( b ) to define a line
y = m x + b
Point – Slope & Slope – Intercept Forms
Point – Slope y = m ( x – a ) + b
Slope – Intercept y = m x + b
EXAMPLE : Find the equation of the line thru ( 1 , 6 ) with a slope ( m ) of2
1
Point – Slope & Slope – Intercept Forms
Point – Slope y = m ( x – a ) + b
Slope – Intercept y = m x + b
EXAMPLE : Find the equation of the line thru ( 1 , 6 ) with a slope ( m ) of
- just replace ( m ) and ( a , b )
y = m ( x – a ) + b
y = ( x – 1 ) + 6
2
1
2
1
a b
Point – Slope & Slope – Intercept Forms
Point – Slope y = m ( x – a ) + b
Slope – Intercept y = m x + b
EXAMPLE : Find the equation of the line thru ( -5 , 1 ) with m =
y = m ( x – a ) + b
3
5
Point – Slope & Slope – Intercept Forms
Point – Slope y = m ( x – a ) + b
Slope – Intercept y = m x + b
EXAMPLE : Find the equation of the line thru ( -5 , 1 ) with m =
- replace ( m ) and ( a , b )
y = m ( x – a ) + b
y = ( x – ( -5 )) + 1
y = ( x + 5 ) + 1
3
5
3
5
3
5
Point – Slope & Slope – Intercept Forms
Point – Slope y = m ( x – a ) + b
Slope – Intercept y = m x + b
EXAMPLE : Find the equation of the line where m = - 3 and b = 2
Point – Slope & Slope – Intercept Forms
Point – Slope y = m ( x – a ) + b
Slope – Intercept y = m x + b
EXAMPLE : Find the equation of the line where m = - 3 and b = 2
- substitute for m and b
y = m x + b
Point – Slope & Slope – Intercept Forms
Point – Slope y = m ( x – a ) + b
Slope – Intercept y = m x + b
EXAMPLE : Find the equation of the line where m = - 3 and b = 2
- substitute for m and b
y = m x + b
y = - 3x + 2
Point – Slope & Slope – Intercept Forms
Point – Slope y = m ( x – a ) + b
Slope – Intercept y = m x + b
EXAMPLE : Find the equation of the line where m = and b =4
1
4
5
Point – Slope & Slope – Intercept Forms
Point – Slope y = m ( x – a ) + b
Slope – Intercept y = m x + b
EXAMPLE : Find the equation of the line where m = and b =
- substitute for m and b
y = m x + b
y = x
4
1
4
5
4
1
4
5
Point – Slope & Slope – Intercept Forms
Point – Slope y = m ( x – a ) + b
Slope – Intercept y = m x + b
EXAMPLE : Find the equation of the line thru ( - 3 , 5 ) and ( 2 , -2 )
Point – Slope & Slope – Intercept Forms
Point – Slope y = m ( x – a ) + b
Slope – Intercept y = m x + b
EXAMPLE : Find the equation of the line thru ( - 3 , 5 ) and ( 2 , -2 )
Steps 1. Find the slope5
7
)3(2
5)2(
12
12
xx
yym
Point – Slope & Slope – Intercept Forms
Point – Slope y = m ( x – a ) + b
Slope – Intercept y = m x + b
EXAMPLE : Find the equation of the line thru ( - 3 , 5 ) and ( 2 , -2 )
Steps 1. Find the slope
2. Pick one of the points ( -3 , 5 ) as ( a , b ) and use the slope you found in step one and substitute into
y = m ( x – a ) + b
5
7
)3(2
5)2(
12
12
xx
yym
Point – Slope & Slope – Intercept Forms
Point – Slope y = m ( x – a ) + b
Slope – Intercept y = m x + b
EXAMPLE : Find the equation of the line thru ( - 3 , 5 ) and ( 2 , -2 )
Steps 1. Find the slope
2. Pick one of the points ( -3 , 5 ) as ( a , b ) and use the slope you found in step one and substitute into
y = m ( x – a ) + b
y = ( x – ( - 3 )) + 5
y = ( x + 3 ) + 5
5
7
)3(2
5)2(
12
12
xx
yym
5
7
5
7
Point – Slope & Slope – Intercept Forms
Point – Slope y = m ( x – a ) + b
Slope – Intercept y = m x + b
EXAMPLE : Find the equation of the line thru ( - 3 , 5 ) and ( 2 , -2 )
Steps 1. Find the slope
2. Pick one of the points ( -3 , 5 ) as ( a , b ) and use the slope you found in step one and substitute into
y = m ( x – a ) + b
y = ( x – ( - 3 )) + 5
y = ( x + 3 ) + 5
5
7
)3(2
5)2(
12
12
xx
yym
5
7
5
7
NOTE : I like to use the point – slope form for these problems. You can use slope – intercept if you choose.
Point – Slope & Slope – Intercept Forms
Point – Slope y = m ( x – a ) + b
Slope – Intercept y = m x + b
EXAMPLE : Find the equation of the line thru ( 6 , - 2 ) and ( 4 , 1 )
Point – Slope & Slope – Intercept Forms
Point – Slope y = m ( x – a ) + b
Slope – Intercept y = m x + b
EXAMPLE : Find the equation of the line thru ( 6 , - 2 ) and ( 4 , 1 )
- I’ll use slope – intercept on this one…
Steps : 1. Find the slope2
3
2
3
64
)2(1
12
12
xx
yym
Point – Slope & Slope – Intercept Forms
Point – Slope y = m ( x – a ) + b
Slope – Intercept y = m x + b
EXAMPLE : Find the equation of the line thru ( 6 , - 2 ) and ( 4 , 1 )
- I’ll use slope – intercept on this one…
Steps : 1. Find the slope2
3
2
3
64
)2(1
12
12
xx
yym
We have part of our answer y = m x + b
2. Substitute m into eq. y = x + b 2
3
Point – Slope & Slope – Intercept Forms
Point – Slope y = m ( x – a ) + b
Slope – Intercept y = m x + b
EXAMPLE : Find the equation of the line thru ( 6 , - 2 ) and ( 4 , 1 )
- I’ll use slope – intercept on this one…
Steps : 1. Find the slope2
3
2
3
64
)2(1
12
12
xx
yym
y = m x + b
y = x + b 2
3
3. Using one of our points as ( x , y ) and substituting into our equation, we can find b
2. Substitute m into eq.
Point – Slope & Slope – Intercept Forms
Point – Slope y = m ( x – a ) + b
Slope – Intercept y = m x + b
EXAMPLE : Find the equation of the line thru ( 6 , - 2 ) and ( 4 , 1 )
- I’ll use slope – intercept on this one…
Steps : 1. Find the slope2
3
2
3
64
)2(1
12
12
xx
yym
y = m x + b
y = x + b
2
3
3. Using one of our points as ( x , y ) and substituting into our equation, we can find b
b
b
b
7
92
62
32
Point – Slope & Slope – Intercept Forms
Point – Slope y = m ( x – a ) + b
Slope – Intercept y = m x + b
EXAMPLE : Find the equation of the line thru ( 6 , - 2 ) and ( 4 , 1 )
- I’ll use slope – intercept on this one…
Steps : 1. Find the slope2
3
2
3
64
)2(1
12
12
xx
yym
y = m x + b
y = x + b
2
3
3. Using one of our points as ( x , y ) and substituting into our equation, we can find b
4. Substitute b
b
b
b
7
92
62
32
Point – Slope & Slope – Intercept Forms
Point – Slope y = m ( x – a ) + b
Slope – Intercept y = m x + b
EXAMPLE : Find the equation of the line thru ( 6 , - 2 ) and ( 4 , 1 )
- I’ll use slope – intercept on this one…
Steps : 1. Find the slope2
3
2
3
64
)2(1
12
12
xx
yym
y = m x + b
y = x + 7
2
3
3. Using one of our points as ( x , y ) and substituting into our equation, we can find b
4. Substitute b
b
b
b
7
92
62
32
Point – Slope & Slope – Intercept Forms
Point – Slope y = m ( x – a ) + b
Slope – Intercept y = m x + b
EXAMPLE : Find the equation of the line thru ( 6 , - 2 ) and ( 4 , 1 )
- I’ll use slope – intercept on this one…
Steps : 1. Find the slope2
3
2
3
64
)2(1
12
12
xx
yym
y = m x + b
y = x + 7
2
3Final Answer :
Finding the slope ( m ) and y – intercept ( b ) from a given equation.
You must solve for y if the equation is not already in y = mx + b form.
Finding the slope ( m ) and y – intercept ( b ) from a given equation.
You must solve for y if the equation is not already in y = mx + b form.
EXAMPLE : Find the slope and y – intercept for y = - 4x + 7
Finding the slope ( m ) and y – intercept ( b ) from a given equation.
You must solve for y if the equation is not already in y = mx + b form.
EXAMPLE : Find the slope and y – intercept for y = - 4x + 7
Since our equation is already in y = mx + b form, we just look for the m and b in their proper position.
Finding the slope ( m ) and y – intercept ( b ) from a given equation.
You must solve for y if the equation is not already in y = mx + b form.
EXAMPLE : Find the slope and y – intercept for y = - 4x + 7
Since our equation is already in y = mx + b form, we just look for the m and b in their proper position.
m b
Finding the slope ( m ) and y – intercept ( b ) from a given equation.
You must solve for y if the equation is not already in y = mx + b form.
EXAMPLE : Find the slope and y – intercept for y = - 4x + 7
Since our equation is already in y = mx + b form, we just look for the m and b in their proper position.
m bm = - 4
b = + 7
Finding the slope ( m ) and y – intercept ( b ) from a given equation.
You must solve for y if the equation is not already in y = mx + b form.
EXAMPLE : Find the slope and y – intercept for 2x + 3y = 10
Finding the slope ( m ) and y – intercept ( b ) from a given equation.
You must solve for y if the equation is not already in y = mx + b form.
EXAMPLE : Find the slope and y – intercept for 2x + 3y = 10
Our equation IS NOT in y = mx + b form, so we need to solve for y…
Finding the slope ( m ) and y – intercept ( b ) from a given equation.
You must solve for y if the equation is not already in y = mx + b form.
EXAMPLE : Find the slope and y – intercept for 2x + 3y = 10
Our equation IS NOT in y = mx + b form, so we need to solve for y…
1023
2 2
1032
xy
xx
yx
- subtracted 2x from both sides
Finding the slope ( m ) and y – intercept ( b ) from a given equation.
You must solve for y if the equation is not already in y = mx + b form.
EXAMPLE : Find the slope and y – intercept for 2x + 3y = 10
Our equation IS NOT in y = mx + b form, so we need to solve for y…
3
10
3
2
3
3
1023
2 2
1032
xy
xy
xx
yx
Divided by 3
Finding the slope ( m ) and y – intercept ( b ) from a given equation.
You must solve for y if the equation is not already in y = mx + b form.
EXAMPLE : Find the slope and y – intercept for 2x + 3y = 10
Our equation IS NOT in y = mx + b form, so we need to solve for y…
3
10
3
2
3
10
3
2
3
3
1023
2 2
1032
xy
xy
xy
xx
yx
Finding the slope ( m ) and y – intercept ( b ) from a given equation.
You must solve for y if the equation is not already in y = mx + b form.
EXAMPLE : Find the slope and y – intercept for 2x + 3y = 10
Our equation IS NOT in y = mx + b form, so we need to solve for y…
3
10
3
2
3
10
3
2
3
3
1023
2 2
1032
xy
xy
xy
xx
yx
m b