Algebra Know-It-ALL

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