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This text is meant to accompany class discussions. It is not everything there is to know about uniform circular motion. It is meant as a  prep for class.

Click for the questions that go with this reading
Calculating the slope

 

Below is a YouTube video showing how to find the slope.

This YouTube video is located at http://youtu.be/wbQoeel9hHo

 

Slopes are positive or negative

 

Positive and negative slope example

Slopes have units

This YouTube video will show you how to calculate the slope's units.

This video can be found on YouTube at http://youtu.be/1pd6qL_DDaI

 

The equation of a stratight line on a graph is expressed in slope-intercept form.

 

y = mx + b

y = y-coordinate for a point on the line.
x = x-coordinate for the same point on a line
m = slope
b = y-intecept ...where the line crosses the vertical axis

For the example graph above, the equation is

Equation

It would be tempting to look at the graph and call the y-intercept 2. The problem with this interpretation is the fact that the graph’s horizontal numbers do not start at zero. Therefore the axis at the left is not the y-axis. The y-axis is where x = 0.

 

Calculating the y-intercept

To calculate the y-intercept, use y = mx +b and solve for b. Pick ANY point on the line to find x and y. Calculate the slope as shown above. Plug these values into y = mx + b and solve for b.

Example

EXAMPLE: from the graph above. x= 60, y = 10 (that’s the first point on the graph, from the data) and m = 4/25.

y-intercept derivation

Therefore the correct equation for the line is

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by Tony Wayne ...(If you are a teacher, please feel free to use these resources in your teaching.)