Rise and Run
Example 1
Find the rise and the run in moving from point P_{1} to point P_{2} on the graph.
Note: In P_{1}(x_{1}, y_{1}), the P stands for â€œpointâ€ and
the small 1 written a bit below and to the
right of P indicates point 1. The small 1 is
called a subscript. It is part of the name
for the point.
Solution
We may find the rise and the run in two ways.
Use the graph:
â€¢ To find the run, on the graph count the number of units of horizontal
change when moving from P_{1} to P_{2}.
The run is 7.
â€¢ To find the rise, count the number of vertical units when moving
from P_{1} to P_{2}.
The rise is 4.
Use algebra:
The coordinates of P_{1} are (3, 1).
The coordinates of P_{2} are (4, 5).
â€¢ To find the rise, subtract the
ycoordinates. That is, find y_{2}  y_{1}.
rise 
= y_{2}
 y_{1} = 5
 1
= 4 
Note that the ycoordinate of the
starting point, y_{1}, is subtracted from
the ycoordinate of the ending point, y_{2}.
â€¢ To find the run, subtract the
xcoordinates. That is, find x_{2}  x_{1}.
rise 
= x_{2}
 x_{1} =
4
 (3)
= 4 + 3 = 7 
Example 2
a. Use the graph to find the rise and the run in moving from (2, 1) to
(4, 3).
b. Use the graph to find the rise and the run in moving the other way, from
(4, 3) to (2, 1).
Solution a. We are starting at (2, 1) and moving to (4,
3).
To find the rise, count the number of vertical units when moving
from (2, 1) to (4, 3).
The rise is 4.
To find the run, count the number of horizontal units when moving
from (2, 1) to (4, 3).
The run is 6.
b. We are starting at (4, 3) and moving to (2, 1).
To find the rise, count the number of vertical units when moving
from (4, 3) to (2, 1).
The rise is 4.
To find the run, count the number of horizontal units when moving
from (4, 3) to (2, 1).
The run is 6.
Note:
The run from (4, 3) to (2, 1) is
6.
This is the opposite of the run from (2, 1) to (4,
3).
