angle of −45°. That means the first line will go “uphill” at 45° as we go to the right, and
the second line will go “downhill” at 45° as we go to the right. The angle between the two
lines will therefore be 45 + 45, or 90°.
If the increments on the s axis are not the same size as those on the t axis, then slopes of
1 and −1 will not appear as “uphill” and “downhill” 45° angles. Depending on which axis
has the larger increments, both lines will be either steeper or less steep. Our advisor, who
claimed that the lines would intersect at a 90° angle, will be mistaken if we draw the lines
on a coordinate system having axes graduated in unequal increments.
- To determine the point where the two lines intersect, we must find an ordered pair of
the form (s,t) that satisfies both equations. Look at the SI forms of the two equations
again:
t=s+ 5
and
t=−s+ 5
If we add the left sides of these equations, we get t+t, which is equal to 2t. If we add the
right sides, we get s+ 5 + (−s)+ 5, which is equal to 10. That means the sum of the two
equations is
2 t= 10
–6 246
4
6
–4
–6
–4 –2
m= 8/3
2
P= (–1,–6)
Q= (2,2)
b= –10/3
(0,–10/3)
u
v
Figure B-6 Illustration for the solution to Prob. 5 in
Chap. 15.
Chapter 15 635
