Algebra Know-It-ALL

Part Two 323

Question 15-3

In Fig. 20-5, how can we determine the slope of line PR? The y-intercept?

Answer 15-3

We know the ordered pairs for the two points as P= (−5,−3) and R= (2,4). Therefore,

Δy= 4 − (−3)

= 4 + 3

= 7

and

Δx= 2 − (−5)

= 2 + 5

= 7

That means Δy/Δx= 7/7 = 1, which is the slope of the line. The y-intercept can be inferred.

Note that if we move to the right from point P by Δx units, we must go up by the same num-

ber of units to stay on the line. If we increase the x-value of point P by 5 units, we arrive at the

y axis, and we’ll be at a point 5 units above the y-value of P. The y-value of P is −3, so 5 more

than that is 2. The y-intercept of line PR is therefore equal to 2.

Question 15-4

Based on Answers 15-1, 15-2, and 15-3, what are the slope-intercept forms of the equations

for lines PQ,QR, and PR?

Answer 15-4

Now that we know the slopes and the y-intercepts of all three lines, we can write the slope-

intercept equations straightaway. Remember the general slope-intercept form for a line in

Cartesian coordinates:

y=mx+b

where x is the independent variable, y is the dependent variable, m is the slope, and b is the

y-intercept. For line PQ, we have

y= (2/5)x− 1

For line QR, we have

y= (5/2)x− 1

For line PR, we have

y=x+ 2