Question 215544
Write a rule for the graph with X = 1, 2, 3, 4 and y = 2, 8, 14, 20. x being the domain and y the range 
<pre><font size =4 color = "indigo"><b>
We plot the points (1,2), (2,8), (3,14), (4,20).

{{{drawing(109,400,-1,5,-1,21, grid(1), rectangle(1,-2,6,22),rectangle(2,-2,6,22),rectangle(3,-2,6,22),rectangle(4,-2,6,22),rectangle(5,-2,6,22),  

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

line(2+.2,8,2-.2,8),line(2,8+.2,2,8-.2),line(2+.2,8-.2,2-.2,8+.2),line(2+.2,8+.2,2-.2,8-.2),

line(3+.2,14,3-.2,14),line(3,14+.2,3,14-.2),line(3+.2,14-.2,3-.2,14+.2),line(3+.2,14+.2,3-.2,14-.2),

line(4+.2,20,4-.2,20),line(4,20+.2,4,20-.2),line(4+.2,20-.2,4-.2,20+.2),line(4+.2,20+.2,4-.2,20-.2) )}}}

We notice that we can draw a straight line through them, like this:

{{{drawing(109,400,-1,5,-1,21, grid(1), rectangle(1,-2,6,22),rectangle(2,-2,6,22),rectangle(3,-2,6,22),rectangle(4,-2,6,22),rectangle(5,-2,6,22),  

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

line(2+.2,8,2-.2,8),line(2,8+.2,2,8-.2),line(2+.2,8-.2,2-.2,8+.2),line(2+.2,8+.2,2-.2,8-.2),

line(3+.2,14,3-.2,14),line(3,14+.2,3,14-.2),line(3+.2,14-.2,3-.2,14+.2),line(3+.2,14+.2,3-.2,14-.2), line(-2,-16,7,38),

line(4+.2,20,4-.2,20),line(4,20+.2,4,20-.2),line(4+.2,20-.2,4-.2,20+.2),line(4+.2,20+.2,4-.2,20-.2) )}}}

So we find the equation of the line that passes through two of them,
say the first two, (1,2) and (2,8)

find the slope, using the formula:

{{{m=(y[2]-y[1])/(x[2]-x[1])=(8-2)/(2-1)=6/1=6}}}

Then substitute in the point-slope equation:

{{{y-y[1]=m(x-x[1])}}}
{{{y-2=6(x-1)}}}
{{{y-2=6x-6}}}
{{{y=6x-4}}}

Now we check to see if (3,14) and (4,20) satisfy the
equation:

Substituting (3,14),
{{{y=6x-4}}}
{{{14=6(3)-4}}}
{{{14=18-4}}}
{{{14=14}}} 

So (3,14) satisfies it and is therefore on the line.

Substituting (4,20),
{{{y=6x-4}}}
{{{20=6(4)-4}}}
{{{20=24-4}}}
{{{20=20}}} 

So (4,20) satisfies it also and is therefore on the line.

Therefore thew correct equation is

{{{y=6x-4}}}

Edwin</pre>