Slope
Lines and Slope
Definition Let
(x_{1},y_{1})
and
(x_{2},y_{2}) be two points then the
slope for those two
points is
rise/run
or
y_{2}  y_{1}
m =
x_{2}  x_{1} 
Example:
For the points (1,2) and (5,3) we have
3 
2
5
m =
=
5 
1
4
Definition
A
line
through a point
P
with slope
m
is the
collection of points
Q
such that the slope between
P
and
Q
is
m. 
Example:
Sketch the line through the point (1,1) with slope
m = 3.
Solution
We plot the point (1,1)
and rise 3 and run 1 from
(1,1) arriving at
(1 + 1,1 + 3) = (2,2)
Then we connect
the dots.
Exercise:
Sketch the line through the point (2,3) with slope
1/2.
Special Cases
Vertical lines have an undefined slope and horizontal lines have a zero slope.
Example:
Without graphing, describe the line through

(3,5) and (3,2)

(1,2) and (3,2)
Solution:

We compute the slope:
2  5 3
m =
= 
3  3 0
which is
undefined, hence the line is vertical.

We compute the slope:
2 
2
0
m =
= 
= 0
3 
2
5
hence
the line is horizontal.
Exercise
Determine whether the points (1,1), (2,4), and
(7,9)
are colinear.
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