Algebra Know-It-ALL

1. Refer to Fig. 17-9. What is the equation of line L in SI form?


2. Refer to Fig. 17-9. What is the equation of line M in SI form?


3. Using the morph-and-mix method, show that the solution to the equations derived in
   Probs. 1 and 2 is x=−3 and y= 0, which shows up as the point (−3, 0).


4. Rotate and mirror Fig. 17-9, obtaining a new graph that shows the system with y as the
   independent variable and x as the dependent variable. Call the transposed line L by the
   new name L, and call the transposed line M by the new name M.


5. Using the graph derived in Prob. 4, what is the equation of line L* in SI form?
   Remember that x is now the dependent variable.


6. Using the graph derived in Prob. 4, what is the equation of line M* in SI form?
   Remember that x is now the dependent variable.


7. Using the morph-and-mix method, show that the solution to the equations derived in
   Probs. 5 and 6 is y= 0, and x=−3, which shows up as the point (0, −3).


8. Suppose we see a linear function where x is the independent variable and y is the
   dependent variable. Let’s call the function f and state it like this:
   f (x)=mx+b

where m is the slope and b is the y-intercept of the graph. In this context, f (x) is just
another name for y. Now imagine that we derive the inverse of this function so y

–6 246

2

4

6

–4

–6

Solution (0,4)

= (–3,0)

(0,–2)

x

y

LM

Figure 17-9 Illustration for Practice Exercises 1 and 2.

Practice Exercises 279