Question

Hello. If I have the following table:

Time(x) 18 27 72 81
Distance (y) 8 12 32 36


How would I create an equation relating the variables in the table?

y=

Please help. I have never done this before?

Answer 1

d = r * t.
8 = r * 18, r = ?.

12 = r * 27, r = ?.

32 = r * 72, r = ?.

Answer 2

check for a common ratio of changes. For example,

(12-8)/(27-18) = 4/11
(32-12)/(72-27) = 20/55 = 4/11
so, it appears that the line has a constant slope of 4/11
Now, using any of the given points, plug into the point-slope form of a line:

y-8 = 4/11 (x-18)
or
11y-88 = 4x-72
11y = 4x+16
y = (4x + 16)/11
etc.

To be thorough, though, you might want to check the other intervals. If the slope changes, then the equation will not be so simple.

Answer 3

I made a typo.
Maybe Henry's solution will be better. Either approach will work if done carefully.

Answer 4

Steve's slope calculations should have resulted in 4/9
so continue with:
y-8 = (4/9)(x-18)