Algebra Know-It-ALL

274 Two-by-Two Linear Graphs

transposing the numbers in the ordered pairs. Once we’ve done these three things, we have a graph of the

two-by-two system with the variables transposed. Figure 17-6 shows the result.

Are you astute?

Do you notice something familiar about the transformation we just performed, as if we’ve done it before?

We have! These maneuvers are the equivalent of mirroring the whole system along the axis correspond-

ing to the line where the values of the independent variable and the values of the dependent variable are

identical. (In this case, that’s the line w=v.) That transformation produces the graph of the inverse of a

relation, as you learned in Chap. 14.

Look at the SI versions of the equations we graphed in Fig. 17-5. For reference, here they are again:

w= 7 v− 10

and

w= (−1/2)v− 5

v

w

Each axis

increment

is 2 units

(11,3)

(–5,0)

Solution =

(–16/3,2/3)

(–10,0)

(1,–12)

–7v+w+ 10 = 0

4 v+ 8w= –40

Figure 17-6 Graphs of − 7 v+w+ 10 = 0 and

4 v+ 8 w=−40 as a two-by-two linear

system where the independent variable is w

and the dependent variable is v. This graph

was obtained by rotating Fig. 17-5 by 90°

counterclockwise, mirroring it right-to-left,

and relabeling the points.