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 Depdendent Variable

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 Dependent Variable

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# Rise and Run

Example 1

Find the rise and the run in moving from point P1 to point P2 on the graph.

Note: In P1(x1, y1), 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 P1 to P2.

The run is 7.

â€¢ To find the rise, count the number of vertical units when moving from P1 to P2. The rise is 4.

Use algebra:

The coordinates of P1 are (-3, 1).

The coordinates of P2 are (4, 5).

â€¢ To find the rise, subtract the y-coordinates. That is, find y2 - y1.
 rise = y2 - y1 = 5 - 1 = 4
Note that the y-coordinate of the starting point, y1, is subtracted from the y-coordinate of the ending point, y2.

â€¢ To find the run, subtract the x-coordinates. That is, find x2 - x1.

 rise = x2 - x1 = 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).