# 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
y-coordinates. That is, find y

_{2} - y

_{1}.

rise |
= y_{2}
- y_{1} = 5
- 1
= 4 |

Note that the y-coordinate of the
starting point, y

_{1}, is subtracted from
the y-coordinate of the ending point, y

_{2}.

â€¢ To find the run, subtract the
x-coordinates. 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).