Question 59322
here's a table. 
x        y
4       14  
8       15.5 
12      17   
16      18.5
How would i find the value of y when x=120?? how about finding the value of x when y=50??  
Your rate of change is the slope between various points.  I checked this out and this is indeed a linear relation.
The formula to find the slope between two points is:
{{{highlight(m=(y2-y1)/(x2-x1))}}} 
You can choose any two points to find the slope, so let's choose the ones without decimals to make it a little easier.
(x1,y1)=(4,14)  and (x2,y2)=(12,17)
{{{m=(17-14)/(12-4)}}}
{{{m=3/8}}}
We can now find the equation of the line using the point-slope formula:{{{highlight(y-y1=m(x-x1))}}}, m=slope,(x1,y1)=any point on the line.
(x1,y1)=(4,14) and m=3/8
{{{y-14=(3/8)(x-4)}}}
{{{8(y-14)=8(3/8)(x-4)}}}
{{{8y-112=3(x-4)}}}
{{{8y-112=3x-12}}}
{{{-3x+8y-112=-3x+3x-12}}}
{{{-3x+8y-112+112=112-12}}}
{{{-3x+8y=100}}}
{{{-(-3x+8y)=-100}}}
{{{3x-8y=-100}}}
:
When x=120
3(120)-8y=-100
360-8y=-100
-360+360-8y=-360-100
-8y=-460
-8y/-8=-460/-8
y=115/2
{{{highlight(y=57.5)}}}
:
When y=50
3x-8(50)=-100
3x-400=-100
3x-400+400=400-100
3x=300
3x/3=300/3
{{{highlight(x=100)}}}
:
If I just blew your mind and you've never seen any of this before, another way you can do this is to plot the points on a graph and using graph paper and a ruler you can approximate the same thing.
:
Happy Calculating!!!