Unformatted text preview: lane determine a unique
line containing those points, as indicated below.
P (x0 , y0 )
Q (x1 , y1 ) To give a sense of the ‘steepness’ of the line, we recall we can compute the slope of the line using
the formula below.
Equation 2.1. The slope m of the line containing the points P (x0 , y0 ) and Q (x1 , y1 ) is:
m= y1 − y0
x1 − x0 provided x1 = x0 .
A couple of notes about Equation 2.1 are in order. First, don’t ask why we use the letter ‘m’ to
represent slope. There are many explanations out there, but apparently no one really knows for
sure.1 Secondly, the stipulation x1 = x0 ensures that we aren’t trying to divide by zero. The reader
is invited to pause to think about what is happening geometrically; the anxious reader can skip
along to the next example.
Example 2.1.1. Find the slope of the line containing the following pairs of points, if it exists. Plot
each pair of points and the line containing them. 1 See www.mathforum.org or www.mathworld.wolfram.com for discussions on this topic. 112 Linear and Quadratic Functions 1. P (0, 0...
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