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Lesson: Finding Equations
Contributed by: Pappal
Sometimes you will need to write the equation
Sometimes you will need to write the equation
given information about the graph.
Sometimes you will need to write the equation
To do this you have to use this equation:
given information about the graph.
Sometimes you will need to write the equation
To do this you have to use this equation:
given information about the graph.
y - y1 = m(x - x1)
Sometimes you will need to write the equation
To do this you have to use this equation:
which is the point-slope form
given information about the graph.
y - y1 = m(x - x1)
Point-slope Form
y - y1 = m(x - x1)
?
y - y1 = m(x - x1)
Point-slope Form
?
To use the point slope form you need three values
y - y1 = m(x - x1)
To use the point slope form you need three values
An x1
y - y1 = m(x - x1)
To use the point slope form you need three values
An x1
y - y1 = m(x - x1)
To use the point slope form you need three values
An x1
An y1
y - y1 = m(x - x1)
To use the point slope form you need three values
An x1
An y1
y - y1 = m(x - x1)
To use the point slope form you need three values
An x1
and an m
An y1
y - y1 = m(x - x1)
To use the point slope form you need three values
An x1
and an m
An y1
y - y1 = m(x - x1)
You will never ever EVER put numbers in for the x and y
y - y1 = m(x - x1)
You will never ever EVER put numbers in for the x and y
y - y1 = m(x - x1)
You will never ever EVER put numbers in for the x and y
y - y1 = m(x - x1)
never
You will never ever EVER put numbers in for the x and y
y - y1 = m(x - x1)
never
You will never ever EVER put numbers in for the x and y
ever
y - y1 = m(x - x1)
never
Mark all variables that will be replaced with numbers
y - y1 = m(x - x1)
y
y1
m
x
x1
Mark all variables that never EVER be replaced with 
y - y1 = m(x - x1)
y
y1
m
x
x1
numbers
So if they give you a point
So if they give you a point
(2,3)
So if they give you a point
and a slope
(2,3)
So if they give you a point
and a slope
(2,3)
4
You will use that to find x1, y1, and m.
So if they give you a point
and a slope
(2,3)
4
You will use that to find x1, y1, and m.
So if they give you a point
and a slope
x1
(2,3)
4
You will use that to find x1, y1, and m.
So if they give you a point
and a slope
x1
(2,3)
4
y1
You will use that to find x1, y1, and m.
So if they give you a point
and a slope
x1
(2,3)
4
m
y1
You will use that to find x1, y1, and m.
So if they give you a point
and a slope
and then plug in those values in
x1
(2,3)
4
m
y1
You will use that to find x1, y1, and m.
So if they give you a point
and a slope
and then plug in those values in
x1
y - y1 = m(x - x1)
(2,3)
4
m
y1
You will use that to find x1, y1, and m.
So if they give you a point
and a slope
and then plug in those values in
x1
y
y - y1 = m(x - x1)
(2,3)
4
m
y1
You will use that to find x1, y1, and m.
So if they give you a point
and a slope
and then plug in those values in
x1
y -
y - y1 = m(x - x1)
(2,3)
4
m
y1
You will use that to find x1, y1, and m.
So if they give you a point
and a slope
and then plug in those values in
x1
y - 3
y - y1 = m(x - x1)
(2,3)
4
m
y1
You will use that to find x1, y1, and m.
So if they give you a point
and a slope
and then plug in those values in
x1
y - 3 =
y - y1 = m(x - x1)
(2,3)
4
m
y1
You will use that to find x1, y1, and m.
So if they give you a point
and a slope
and then plug in those values in
x1
y - 3 = 4
y - y1 = m(x - x1)
(2,3)
4
m
y1
You will use that to find x1, y1, and m.
So if they give you a point
and a slope
and then plug in those values in
x1
y - 3 = 4(
y - y1 = m(x - x1)
(2,3)
4
m
y1
You will use that to find x1, y1, and m.
So if they give you a point
and a slope
and then plug in those values in
x1
y - 3 = 4(x
y - y1 = m(x - x1)
(2,3)
4
m
y1
You will use that to find x1, y1, and m.
So if they give you a point
and a slope
and then plug in those values in
x1
y - 3 = 4(x -
y - y1 = m(x - x1)
(2,3)
4
m
y1
You will use that to find x1, y1, and m.
So if they give you a point
and a slope
and then plug in those values in
x1
y - 3 = 4(x - 2
y - y1 = m(x - x1)
(2,3)
4
m
y1
You will use that to find x1, y1, and m.
So if they give you a point
and a slope
and then plug in those values in
x1
y - 3 = 4(x - 2)
y - y1 = m(x - x1)
(2,3)
4
m
y1
y - y1 = m(x - x1)
x1 = 1
y1 = 4
m = 5
y
-
4
?
=
5
?
(
x
-
1
?
)
Slope:
Point:
(
5
1
,
4
)
y - y1 = m(x - x1)
x1 = 3
y1 = 8
m = 2
y
-
8
?
=
2
?
(
x
-
3
?
)
Slope:
Point:
(
2
3
,
8
)
y - y1 = m(x - x1)
x1 =
y1 =
m =
y
1
?
9
?
5
?
-
9
=
5
(
x
-
1
)
Slope:
Point:
(
5
1
,
9
)
y - y1 = m(x - x1)
x1 =
y1 =
m =
y
-2
?
-3
?
-6
?
+
3
=
-6
(
x
+
2
)
Slope:
Point:
(
-6
-2
,
-3
)
y - y1 = m(x - x1)
x1 = 6
y1 = 1
m = 4
y
-
1
=
4
(
x
-
6
)
Slope:
Point:
(
4
?
6
?
,
1
?
)
Sometimes they will give you 2 points
Sometimes they will give you 2 points
and ask you to find the equation
Sometimes they will give you 2 points
and ask you to find the equation
( 7 , 3 )
Sometimes they will give you 2 points
and ask you to find the equation
( 7 , 3 )
( 6 , 2 )
You need an x1, y1, and an m
Sometimes they will give you 2 points
and ask you to find the equation
( 7 , 3 )
( 6 , 2 )
You need an x1, y1, and an m
Sometimes they will give you 2 points
and ask you to find the equation
x1
( 7 , 3 )
( 6 , 2 )
You need an x1, y1, and an m
Sometimes they will give you 2 points
and ask you to find the equation
x1
( 7 , 3 )
( 6 , 2 )
y1
You need an x1, y1, and an m
Sometimes they will give you 2 points
and ask you to find the equation
x1
( 7 , 3 )
( 6 , 2 )
y1
no m?
You need an x1, y1, and an m
Sometimes they will give you 2 points
To find the m you must use the slope formula
and ask you to find the equation
x1
( 7 , 3 )
( 6 , 2 )
y1
You need an x1, y1, and an m
Sometimes they will give you 2 points
To find the m you must use the slope formula
m = 
and ask you to find the equation
x1
y2 - y1
x2 - x1
( 7 , 3 )
( 6 , 2 )
y1
You need an x1, y1, and an m
Sometimes they will give you 2 points
To find the m you must use the slope formula
m = 
and ask you to find the equation
x1
x2
y2 - y1
x2 - x1
( 7 , 3 )
( 6 , 2 )
y1
You need an x1, y1, and an m
Sometimes they will give you 2 points
To find the m you must use the slope formula
m = 
and ask you to find the equation
x1
x2
y2 - y1
x2 - x1
( 7 , 3 )
( 6 , 2 )
y2
y1
You need an x1, y1, and an m
Sometimes they will give you 2 points
To find the m you must use the slope formula
m = 
and ask you to find the equation
x1
x2
y2 - y1
x2 - x1
( 7 , 3 )
( 6 , 2 )
=
y2
y1
You need an x1, y1, and an m
Sometimes they will give you 2 points
To find the m you must use the slope formula
m = 
and ask you to find the equation
x1
x2
y2 - y1
x2 - x1
( 7 , 3 )
( 6 , 2 )
=
y2
y1
You need an x1, y1, and an m
Sometimes they will give you 2 points
To find the m you must use the slope formula
m = 
and ask you to find the equation
x1
x2
y2 - y1
x2 - x1
( 7 , 3 )
( 6 , 2 )
=
2
y2
y1
You need an x1, y1, and an m
Sometimes they will give you 2 points
To find the m you must use the slope formula
m = 
and ask you to find the equation
x1
x2
y2 - y1
x2 - x1
( 7 , 3 )
( 6 , 2 )
=
2 -
y2
y1
You need an x1, y1, and an m
Sometimes they will give you 2 points
To find the m you must use the slope formula
m = 
and ask you to find the equation
x1
x2
y2 - y1
x2 - x1
( 7 , 3 )
( 6 , 2 )
=
2 - 3
y2
y1
You need an x1, y1, and an m
Sometimes they will give you 2 points
To find the m you must use the slope formula
m = 
and ask you to find the equation
x1
x2
y2 - y1
x2 - x1
( 7 , 3 )
( 6 , 2 )
=
2 - 3
6
y2
y1
You need an x1, y1, and an m
Sometimes they will give you 2 points
To find the m you must use the slope formula
m = 
and ask you to find the equation
x1
x2
y2 - y1
x2 - x1
( 7 , 3 )
( 6 , 2 )
=
2 - 3
6 - 
y2
y1
You need an x1, y1, and an m
Sometimes they will give you 2 points
To find the m you must use the slope formula
m = 
and ask you to find the equation
x1
x2
y2 - y1
x2 - x1
( 7 , 3 )
( 6 , 2 )
=
2 - 3
6 - 7
y2
y1
You need an x1, y1, and an m
Sometimes they will give you 2 points
To find the m you must use the slope formula
m = 
and ask you to find the equation
x1
x2
y2 - y1
x2 - x1
( 7 , 3 )
( 6 , 2 )
=
2 - 3
6 - 7
y2
y1
=
You need an x1, y1, and an m
Sometimes they will give you 2 points
To find the m you must use the slope formula
m = 
and ask you to find the equation
x1
x2
y2 - y1
x2 - x1
( 7 , 3 )
( 6 , 2 )
=
2 - 3
6 - 7
y2
y1
=
-1
-1
You need an x1, y1, and an m
Sometimes they will give you 2 points
To find the m you must use the slope formula
m = 
and ask you to find the equation
x1
x2
y2 - y1
x2 - x1
( 7 , 3 )
( 6 , 2 )
=
2 - 3
6 - 7
y2
y1
=
-1
-1
=
You need an x1, y1, and an m
Sometimes they will give you 2 points
To find the m you must use the slope formula
m = 
and ask you to find the equation
x1
x2
y2 - y1
x2 - x1
( 7 , 3 )
( 6 , 2 )
=
2 - 3
6 - 7
y2
y1
=
-1
-1
=
1
You need an x1, y1, and an m
Sometimes they will give you 2 points
To find the m you must use the slope formula
m = 
and ask you to find the equation
y2 - y1
x2 - x1
( 7 , 3 )
( 6 , 2 )
=
2 - 3
6 - 7
=
-1
-1
=
1
x1 = 7
You need an x1, y1, and an m
Sometimes they will give you 2 points
To find the m you must use the slope formula
m = 
and ask you to find the equation
y2 - y1
x2 - x1
( 7 , 3 )
( 6 , 2 )
=
2 - 3
6 - 7
=
-1
-1
=
1
x1 = 7
y1 = 3
You need an x1, y1, and an m
Sometimes they will give you 2 points
To find the m you must use the slope formula
m = 
and ask you to find the equation
y2 - y1
x2 - x1
( 7 , 3 )
( 6 , 2 )
=
2 - 3
6 - 7
=
-1
-1
=
1
x1 = 7
m = 1
y1 = 3
You need an x1, y1, and an m
Sometimes they will give you 2 points
To find the m you must use the slope formula
m = 
and ask you to find the equation
y2 - y1
x2 - x1
( 7 , 3 )
( 6 , 2 )
=
2 - 3
6 - 7
=
y
-1
-1
=
1
x1 = 7
m = 1
y1 = 3
You need an x1, y1, and an m
Sometimes they will give you 2 points
To find the m you must use the slope formula
m = 
and ask you to find the equation
y2 - y1
x2 - x1
( 7 , 3 )
( 6 , 2 )
=
2 - 3
6 - 7
=
y - 
-1
-1
=
1
x1 = 7
m = 1
y1 = 3
You need an x1, y1, and an m
Sometimes they will give you 2 points
To find the m you must use the slope formula
m = 
and ask you to find the equation
y2 - y1
x2 - x1
( 7 , 3 )
( 6 , 2 )
=
2 - 3
6 - 7
=
y - 3 
-1
-1
=
1
x1 = 7
m = 1
y1 = 3
You need an x1, y1, and an m
Sometimes they will give you 2 points
To find the m you must use the slope formula
m = 
and ask you to find the equation
y2 - y1
x2 - x1
( 7 , 3 )
( 6 , 2 )
=
2 - 3
6 - 7
=
y - 3 =
-1
-1
=
1
x1 = 7
m = 1
y1 = 3
You need an x1, y1, and an m
Sometimes they will give you 2 points
To find the m you must use the slope formula
m = 
and ask you to find the equation
y2 - y1
x2 - x1
( 7 , 3 )
( 6 , 2 )
=
2 - 3
6 - 7
=
y - 3 = 1
-1
-1
=
1
x1 = 7
m = 1
y1 = 3
You need an x1, y1, and an m
Sometimes they will give you 2 points
To find the m you must use the slope formula
m = 
and ask you to find the equation
y2 - y1
x2 - x1
( 7 , 3 )
( 6 , 2 )
=
2 - 3
6 - 7
=
y - 3 = 1(
-1
-1
=
1
x1 = 7
m = 1
y1 = 3
You need an x1, y1, and an m
Sometimes they will give you 2 points
To find the m you must use the slope formula
m = 
and ask you to find the equation
y2 - y1
x2 - x1
( 7 , 3 )
( 6 , 2 )
=
2 - 3
6 - 7
=
y - 3 = 1(x
-1
-1
=
1
x1 = 7
m = 1
y1 = 3
You need an x1, y1, and an m
Sometimes they will give you 2 points
To find the m you must use the slope formula
m = 
and ask you to find the equation
y2 - y1
x2 - x1
( 7 , 3 )
( 6 , 2 )
=
2 - 3
6 - 7
=
y - 3 = 1(x - 
-1
-1
=
1
x1 = 7
m = 1
y1 = 3
You need an x1, y1, and an m
Sometimes they will give you 2 points
To find the m you must use the slope formula
m = 
and ask you to find the equation
y2 - y1
x2 - x1
( 7 , 3 )
( 6 , 2 )
=
2 - 3
6 - 7
=
y - 3 = 1(x - 7
-1
-1
=
1
x1 = 7
m = 1
y1 = 3
You need an x1, y1, and an m
Sometimes they will give you 2 points
To find the m you must use the slope formula
m = 
and ask you to find the equation
y2 - y1
x2 - x1
( 7 , 3 )
( 6 , 2 )
=
2 - 3
6 - 7
=
y - 3 = 1(x - 7)
-1
-1
=
1
x1 = 7
m = 1
y1 = 3
You need an x1, y1, and an m
Sometimes they will give you 2 points
To find the m you must use the slope formula
m = 
and ask you to find the equation
y2 - y1
x2 - x1
( 7 , 3 )
( 6 , 2 )
=
2 - 3
6 - 7
=
y - 3 = 1(x - 7)
-1
-1
=
1
x1 = 7
m = 1
y1 = 3
y2 =
x1 =
y1 =
x2 =
m =
m = 
7
?
y2 - y1
x2 - x1
8
?
4
?
3
?
7
4
-
-
8
3
=
-1
?
1
?
Point 1:
Point 2:
(
(
3
4
,
,
8
7
)
)
y2 =
x1 =
y1 =
x2 =
m =
m = 
4
?
y2 - y1
x2 - x1
1
?
7
?
2
?
4
7
-
-
1
2
=
3
?
5
?
Point 1:
Point 2:
(
(
2
7
,
,
1
4
)
)
y2 =
x1 =
y1 =
x2 =
m =
m = 
8
?
y2 - y1
x2 - x1
9
?
7
?
6
?
8
7
-
-
9
6
=
-1
?
1
?
Point 1:
Point 2:
(
(
6
7
,
,
9
8
)
)
They may ask you for the equation of a line
They may ask you for the equation of a line
parallel to a given line
They may ask you for the equation of a line
parallel to a given line
y = 3x +2
given line
They may ask you for the equation of a line
parallel to a given line
y = 3x +2
through a given point
They may ask you for the equation of a line
parallel to a given line
y = 3x +2
through a given point
(1,4)
given point
They may ask you for the equation of a line
parallel to a given line
y = 3x +2
through a given point
x1
(1,4)
y1
They may ask you for the equation of a line
parallel to a given line
y = 3x +2
through a given point
m
x1
(1,4)
y1
They may ask you for the equation of a line
parallel to a given line
y = 3x +2
through a given point
m
x1
(1,4)
y1
y - y1 = m(x - x1)
They may ask you for the equation of a line
parallel to a given line
y = 3x +2
through a given point
m
x1
(1,4)
y1
y - y1 = m(x - x1)
y - 4 = 3(x - 1)
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