Question 342353
<pre><b>
  x	-3	-2	1	3	4
f(x)	0	 3	12	18	21

One way is to plot the points and see what the graph looks like

{{{drawing(176,400,-4,7,-3,22, graph(176,400,-4,7,-3,22),

line(-3,0+.1,-3,0-.1),line(-3+.1,0,-3-.1,0),line(-3+.1,0+.1,-3-.1,0-.1),
line(-3+.1,0-.1,-3-.1,0+.1),

line(-2,3+.1,-2,3-.1),line(-2+.1,3,-2-.1,3),line(-2+.1,3+.1,-2-.1,3-.1),
line(-2+.1,3-.1,-2-.1,3+.1),

line(1,12+.1,1,12-.1),line(1+.1,12,1-.1,12),line(1+.1,12+.1,1-.1,12-.1),
line(1+.1,12-.1,1-.1,12+.1),

line(3,18+.1,3,18-.1),line(3+.1,18,3-.1,18),line(3+.1,18+.1,3-.1,18-.1),
line(3+.1,18-.1,3-.1,18+.1),

line(4,21+.1,4,21-.1),line(4+.1,21,4-.1,21),line(4+.1,21+.1,4-.1,21-.1),
line(4+.1,21-.1,4-.1,21+.1),

locate(-3.9,1.2,"(-3,0)"),locate(-3.9,4.5,"(-2,3)"),locate(1,12,"(1,12)"),locate(3,18,"(3,18)"),locate(4,21,"(4,21)") 


   )}}}

Hmm!  Looks like a straight line could be drawn through all
5 of those points.  I'll get my ruler and green pen and see:

{{{drawing(176,400,-4,7,-3,22, graph(176,400,-4,7,-3,22),
green(line(-10,-21,9,36)),
line(-3,0+.1,-3,0-.1),line(-3+.1,0,-3-.1,0),line(-3+.1,0+.1,-3-.1,0-.1),
line(-3+.1,0-.1,-3-.1,0+.1),

line(-2,3+.1,-2,3-.1),line(-2+.1,3,-2-.1,3),line(-2+.1,3+.1,-2-.1,3-.1),
line(-2+.1,3-.1,-2-.1,3+.1),

line(1,12+.1,1,12-.1),line(1+.1,12,1-.1,12),line(1+.1,12+.1,1-.1,12-.1),
line(1+.1,12-.1,1-.1,12+.1),

line(3,18+.1,3,18-.1),line(3+.1,18,3-.1,18),line(3+.1,18+.1,3-.1,18-.1),
line(3+.1,18-.1,3-.1,18+.1),

line(4,21+.1,4,21-.1),line(4+.1,21,4-.1,21),line(4+.1,21+.1,4-.1,21-.1),
line(4+.1,21-.1,4-.1,21+.1),

locate(-3.9,1.2,"(-3,0)"),locate(-3.9,4.5,"(-2,3)"),locate(1,12,"(1,12)"),locate(3,18,"(3,18)"),locate(4,21,"(4,21)") 


   )}}}

Sure looks like a straight line to me.  So I'll just find the equation
of the line that goes through, say, the first two points (any two
of the points would do).

(-3,0), (-2,3)

{{{m=(y[2]-y[1])/(x[2]-x[1])}}}

{{{m=((3)-(0))/((-2)-(-3))}}}

{{{m=3/(-2+3)}}}

{{{m=3/(-1)}}}

{{{m=3}}}

Then I'll substitute that in the point-slope form:

{{{y-y[1]=m(x-x[1])}}}

{{{y-0=3(x-(-3))}}}

{{{y=3(x+3)}}}

{{{y=3x+9}}}

That's the answer.

Let's check to see if it works with all 5 points:

Substituting (-3,0)

{{{y=3x+9}}}
{{{0=3(-3)+9}}}
{{{0=-9+9}}}
{{{0=0}}}

Substituting (-2,3)

{{{y=3x+9}}}
{{{3=3(-2)+9}}}
{{{3=-6+9}}}
{{{3=3}}}

Substituting (1,12)

{{{y=3x+9}}}
{{{12=3(1)+9}}}
{{{12=3+9}}}
{{{12=12}}}

Substituting (3,18)

{{{y=3x+9}}}
{{{18=3(3)+9}}}
{{{18=9+9}}}
{{{18=18}}}

Substituting (4,21)

{{{y=3x+9}}}
{{{21=3(4)+9}}}
{{{21=12+9}}}
{{{21=21}}}

Yeppers, it works for all 5 points,
so the equation is 

y = 3x + 9

Edwin</pre>