How do I find the y-intercept from a table? I know if the table has the x value as 0, and it gives the y value, then that is the y intercept coordinates. But I'm talking about if it doesn't show a zero value for x.

Question

How do I find the y-intercept from a table?  I know if the table has the x value as 0, and it gives the y value, then that is the y intercept coordinates.  But I'm talking about if it doesn't show a zero value for x.

So for example, if my table is something like this:

Month      Weight Loss in pounds

4          20.8
5          26
6          31.2
7          36.4

I know how to write the equation, but they always ask the y-intercept question BEFORE they ask for the equation, so I'm wondering if there is a way to do it?   I'm a little stumped here.

I know this is direction variation so there isn't a y-intercept, but I couldn't think of another example - my main question is how to find the y intercept from a table when there is no x=0 value showing. 
Thank you.

Scott · Answer

you can "project" along the line

find the slope
... in this case, 5.2

pick a point
... (6,31.2)

y - (m x) = b ... 31.2 - (6 * 5.2) = 0

the line goes through the origin, which would be expected (in this case)
... weight loss isn't counted until the diet starts ... zero loss at zero time