Part Two 325
Question 15-8
How can we determine the point-slope form of the equation for line PR, based on the coordi-
nates of point R and the slope of the line?
Answer 15-8
We know that R= (2, 4), so x 0 = 2 and y 0 = 4. We also know that for line PR, the slope m is
equal to 1. Therefore, the point-slope equation for line PR is
y− 4 =x− 2
Question 15-9
It’s intuitively obvious that the equations we derived in Answers 15-7 and 15-8 must represent
the same line. How can we prove it by showing that the equations are equivalent?
Answer 15-9
If we can convert one of the equations into the other using the rules for equation morphing,
it will prove that the equations are equivalent. Let’s start with
y+ 3 =x+ 5
We can subtract 7 from each side, getting
y− 4 =x− 2
That’s all there is to it!
Question 15-10
Starting with the slope-intercept forms, how can we morph the equations for lines PQ,QR,
andPR in Fig. 20-5 into the form
ax+by=c
where a,b, and c are integer constants?
Answer 15-10
From Answer 15-4, the slope-intercept form of the equation for line PQ is
y= (2/5)x− 1
We can multiply through by 5 to obtain
5 y= 2 x− 5
Subtracting 2x from each side gives us
− 2 x+ 5 y=− 5