Friday, October 11, 2013

Slope, Distance and More

Ski Vacation? Nope, this is serious stuff; it’s about finding the slope of a line, finding the equation of a line with a given slope, finding the equation of the tangent line to a function, finding the distance between two points, finding the quadrant of a point, finding the midpoint of a line segment.  That’s a lot of lines and points, and functions too.

Basically, you have to follow the rules, no tricks, just knowing how to use it all.   We’ve added the line features to help you sort this through…step by step

Let’s start with a couple of examples.

Find the equation of a line given a point and slope m (click here):

All it takes is solving a linear equation to compute the y=intercept b

Let’s continue with the most challenging one, the tangent line.  It is only challenging b/c it requires derivation, and it is using all the line features we’ve seen so far.  So we have a function and a point, we have to start by finding the slope (that’s where we derivate), compute the slope at a given point, now we can find the tangent line ( slope + point = line)

Here is an example (click here):

You can check out more examples here.



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  17. The slope of a line is called the gradient . It may be defined as: The change in vertical distance or elevation* over a given horizontal distance, or the change in horizontal distance over a given vertical distance; The vertical angle made by the sloping line and a horizontal line.
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  18. In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line. ... The direction of a line is either increasing, decreasing, horizontal or vertical.
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