How do you find a function equation from two sample equations like f(-3)=1 and f(3)=2?

Question

I tried solving it like a regular equation, but I didn't get an answer.

Guess and check is too tedious, so I would like to avoid that method if possible.

Answer 1

Grace, this one isn't difficult, once you think about graphing it.

So graph the points (-3,1) and (3,2). What do you think about them? Can you think of any sort of figure that connects two points?

So you probably know the y=mx + b standard equation form for a line. Can you get from your two points to this equation? Think: m = slope = rise/run. Calculate the rise (2-1=1) and the run (3-(-3)=6), then the slope.

Next, plug this value for m (=1/6) into the standard equation form, and throw in either one of your (x,y) points -- let's say, use the (-3,1):

y = (1/6)x + b

1 = (1/6)(-3) + b

1 = (-1/2) + b

b = (3/2)

Put it all together:

One possible equation (the simplest, a straight line) is the line: y = (1/6)x + (3/2).

There are, of course, an infinity of other equations (definitions of a function f) which will include these two points. But worry about that later!