Chapter 15
- We have these two ordered pairs defining the points P and Q, respectively:
P= (u 1 ,v 1 )= (−1,−6)
and
Q= (u 2 ,v 2 )= (2, 2)
The slope m is equal to the difference in the dependent-variable coordinates divided by
the difference in the independent-variable coordinates, or Δv/Δu. If we move along the
line from P to Q, we find the slope on the basis of the ratio between the differences in the
point values with the “destination” values listed first:
m= (v 2 −v 1 ) / (u 2 −u 1 )
Plugging in the values v 2 = 2, v 1 =−6,u 2 = 2, and u 1 =−1, we get
m= [2 − (−6)] / [2 − (−1)]
= (2 + 6) / (2 + 1)
= 8/3
- We still have the same two points, defined by the same two ordered pairs. Points P and Q,
respectively, are still defined by
P= (u 1 ,v 1 )= (−1,−6)
and
Q= (u 2 ,v 2 )= (2, 2)
If we want to go from Q to P rather than from P to Q, we must reverse the order of v 1 and
v 2 in the numerator of the slope equation, and we must also reverse the order of u 1 and u 2
in the denominator. When we do that, we get
m= (v 1 −v 2 ) / (u 1 −u 2 )
= (− 6 − 2) / (− 1 − 2)
=−8 / (−3)
= 8/3
The slope in either direction is equal to the difference in the v values divided by the differ-
ence in the u values, or Δv/Δu. Reversing the direction in which we move along the line
simply multiplies both Δv and Δu by −1. The ratio turns out the same either way.
Chapter 15 633