Rise and Run

Mr. Richard GillDr. Marcia Tharp

Introduction to the Cartesian Coordinate System

  In this unit we introduce the Cartesian coordinate system sometimes referred to as the rectangular coordinate system. A solid foundation in the Cartesian coordinate system will be very important to your success in reading graphs and creating graphs in the near future.

In the following example we calculate rise and run with the formulas: rise= y2 - y1 and run = x2 – x1 where (x1, y1) is the first point

and (x2,y2) is the second.

Example 1Find the rise and the run for the two points in the sketch.Click here to view the graph and complete the exercise.

• Did you get the correct answer?

Solution:rise= y2 - y1 =3-(-1)=4 run = x2 – x1 = 4-2=2

Example 2Find the rise and the run for each point in the sketchClick here to view the sketch to complete the exercise

Find the rise and the run for each point in the sketch.

Solution Example 2

Rise= y2- y1= -2 – 0 = -2

Run = x2- x1= 1-(-3) = 4

Example 3

Find the rise and the run moving

from P(3,-5) to Q(-5,8).

Solution Example 3

Rise= y2- y1= 8 – (-5) = 8 + 5 =13

Run = x2- x1= -5 – 3 = -5+ -3= -8

Example 4

Find the rise and the run moving from

Q(-5,8) to P(3,-5).

Solution Example 4

Rise= y2- y1= -5 - 8 = -5+ -8 = - 13

Run = x2- x1= 3-(-5) = 3 + 5 = 8

In the examples 3 and 4 above note that the rise and the run change signs when you change directions but the ratio of rise to run in each case would be –(13/8). The ratio of rise to run is called the slope of a line and is a very powerful tool to measure the steepness of the line or its rate of change.

Go on to learn about thedistance formula.