Finding The Slope Of A Line That…
. . . Is Pictured on a graph
slope  m 
rise
run
Pick two points on a line. From
the first point count how far the
line rises up and runs to the right.
If you drop down it is a negative
rise or negative number.
If you go left it is a negative run
or negative number.
m =  2  2
m =1
5
1
. . . Passes through two points:
slope  m 
y2  y1
x2  x1
(x1, y1) and (x2, y2)
(6, 8) and (3, 5)
(x1, y1) and (x2, y2)
(-7, -2) and (-4, -9)
y 2  y1 5  8  3 3



x2  x1 3  6  2 2
y 2  y1  9  (2)  9  2  7



x2  x1  4  (7)  4  7
3
. . . Is in Slope-Intercept Form: y = mx +b
Slope is always m, which is the
coefficient of the x-term
(number next to the x variable).
y = 5x + 9
m=5
y = -3x + 18 m = -3
. . . Is in Standard Form: Ax + By = C
Change to slopeintercept form by
isolating y. Now the
slope is coefficient
of the x-term.
Tri-County Technical College
6x + 3y = 21
m=–3
– 4x + 5y = 20
m=
3y = – 6x + 21
5y = 20 + 4x
(subtract 6x from both sides)
(add 4x to both sides)
4
y=4+ x
5
(divide everything by 5)
y = 7 – 3x
(divide everything by 3)
May 2006
Created by Tonia Faulling
4
5
Finding The Slope Of A Line That…
. . . Is Horizontal: y = a
Slope of a horizontal line is
always equal to zero, m = 0.
y = 13
y= 
m=0
23
4
m =0
. . . Is Vertical: x = b
Slope of a vertical line
is always undefined,
m = undefined.
x = – 2008
x=
m = undefined
1
3
m = undefined
. . . Is Parallel to another line:
If two lines are parallel
they have the exactly
the same slope.
These two lines are parallel.
y = 8x + 16
m=8
Find the slope of the line
parallel to y = 3 – x.
m = –1
y = – 1 + 8x
m=8
. . . Is Perpendicular to another line:
If two lines are
These two lines are perpendicular.
1
perpendicular they
y = 2x + 16 y = – x + 21
have the slopes that are
2
1
negative reciprocals of
m=2
m=–
2
each other.
Find the slope of the line
perpendicular to
y=7+
1
x.
9
m=–9
* * * * * Quick check for the sign of the slope. * * * * *
Slope is Positive if the line starts low goes
high from left to right.
Tri-County Technical College
May 2006
Slope is Negative if the line starts high
goes low from left to right.
Created by Tonia Faulling