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When looking at a line on the coordinate grid we can visualize a right triangle, where our original line is the hypotenuse.

We can use the legs to compute rise over run rise run , the slope of the line. Roofers use rise over run rise run to determine the pitch or slope of a roof.

Line graph with 'rise' and 'run' between 2 points

This activity might not be viewable on your mobile device. Interactive exercise. Assistance may be required. Use the Slope Rise Run applet below to gather some data to answer a few questions.

Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)

Click on the blanks to check possible answers.

	Point A	Point B	Rise	Run	Slope
Positive Slope	Interactive button. Assistance may be required. _______ (8,2)	Interactive button. Assistance may be required. _______ (6, -2)	Interactive button. Assistance may be required. _______ 4	Interactive button. Assistance may be required. _______ 2	Interactive button. Assistance may be required. _______ 2
Negative Slope	Interactive button. Assistance may be required. _______ (3,1)	Interactive button. Assistance may be required. _______ (8,-2)	Interactive button. Assistance may be required. _______ 3	Interactive button. Assistance may be required. _______ -5	Interactive button. Assistance may be required. _______ -0.6
Any Slope	Interactive button. Assistance may be required. _______ (3,1)	Interactive button. Assistance may be required. _______ (2,-3)	Interactive button. Assistance may be required. _______ 4	Interactive button. Assistance may be required. _______ 1	Interactive button. Assistance may be required. _______ 4
Slope of 0	Interactive button. Assistance may be required. _______ (3,1)	Interactive button. Assistance may be required. _______ (1,1)	Interactive button. Assistance may be required. _______ 0	Interactive button. Assistance may be required. _______ 2	Interactive button. Assistance may be required. _______ 0
Slope of ∞	Interactive button. Assistance may be required. _______ (3,1)	Interactive button. Assistance may be required. _______ (3,3)	Interactive button. Assistance may be required. _______ 2	Interactive button. Assistance may be required. _______ 0	Interactive button. Assistance may be required. _______ ∞

Answer the following questions.

When the slope of your line was negative, what were the signs of the Rise and Run?

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One was negative and the other positive.
Why do you think that was the case?

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When counting from one point to the next we went in one negative direction, either to the left or down…but not both.

So, when using the ratio rise over run rise run to compute slope it is important to remember to pay attention to the direction when counting between points.

Was it possible to use the ratio rise over run rise run to find the slope when the line was horizontal or vertical? Why?

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No, because you couldn't form the right triangle.
How do the coordinate points relate to the rise and the run values?

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When the x-values are subtracted it looks like a run, moving left to right or right to left. When the y-values are subtracted the movement is up and down so it appears to rise.

So, subtracting the y-values from each point gives us the rise, while subtracting the x-values gives us the run. Sounds like a formula, doesn't it?

slope = m = rise over run rise run = (y sub one minus y sub two) over (x sub 1 minus x sub 2) y₁ − y₂ x₁ − x₂

It looks like the difference of the y-values of both points is the rise and the difference of the x-values of each point is the run. Remember to use the same point for the first value for both the x and the y.