Positive Slope Negative Slope Zero Slope Undefined Slope
(Skiing up) (Skiing down) (Skiing horizontally) (Skiing vertically is impossible,
thus, “undefined”)
The slope of a line is a measure of how much the line
slants
and in which direction it is slanting.
The letter “ m” is used to designate slope, and we assume all lines enter the graph from the left.
Think of ski slopes to help understand the slope of a line:
m = 2
(Line slants up to the right,
so the slope is positive)
m = -0.8
(Line slants down to the right,
so
the slope is negative)
m = 0
(Line slants neither up nor
down, so the slope is zero)
Horizontal lines always
have a slope of zero.
m = undefined
(the slope is undefined )
Vertical lines have
slopes that are undefined.
A line consists of two or more points, and in the x-y coordinate plane, the slope of a line is a ratio of the difference in the y values
to the difference in the x values of two points. The difference in y values is called “rise”, and the difference in x values is the “run”.
We use the letter “m” for slope; if the coordinates of the two points are (x
1
, y
1
) and (x
2
, y
2
), then the slope (m) =
=
Given Two Points
Given an Equation
Given a Graph
Use the Slope Formula:
m =
Put equation into slope-intercept form:
y = mx + b
Count from one point on the line to
another, using the Rise and the Run.
Example
(1, -4) and (-2, 3)
First label the x and y coordinates and
then plug them into the slope formula:
(1, -4) (-2, 3)
(x
1
, y
1
) (x
2
, y
2
)
m =
m =
=
Slope is the rise divided by the run;
the rise = 7 and the run = –3, so slope
m =
=
= –
Example
3x – y = 5
Change the equation into the slope-
intercept form, y = mx + b, so it will
be easy to identify the slope (m) and
the y-intercept (b).
Add -3x to both sides of the equation
– y = –3x + 5
Divide both sides of the equation by -1
=
+
y = 3x – 5
The coefficient of x is the slope of the
line, or m. In rise and run terms, the
rise is 3 and the run is 1. (3 = 3/1)
The slope is 3 and the y-intercept is -5
Example
Using the graph below -
y
–2
+1 x
–2
+1
–2
+1
Count from one point to the next: go down
2 units, then go to the right 1 unit.
DOWN is a negative rise. RIGHT is a
positive run. The rise over the run is (-2)
over (+1); therefore, the slope is -2.
m =
=
= –2
