Where should the hooks go?
We have a wall and we want to hang 18 pictures frames. We want to find where to hang the hooks.
We have two values in the table:
the 3rd hook is at 12 ft and the 7th hook is at 26 ft
This is:
In order to find the values between the 3rd and 7th we are going to count the places between them:
7 - 3 = 4
There are four places between 12 and 26.
Since the distance between is
26ft - 12ft = 14ft
the division between 14 by 4 is:
14ft ÷ 4 = 3.5ft
Then, from hook to hook there is a difference of 3.5ft.
Now we can fill the table:
For the other values, adding and substracting 3.5, we have that
Now, we have all the information to fill completely the table;
It just have to be a 3.5 of difference between spaces
Since it is increasing a distance of 3.5ft from hook to hook, then the distance is given by the equation:
d = 3.5n + ??
where n is the hook number
We want to find the unkown number ?? in order to find the complete equation.
For the first hook we have that n = 1 and distance is 5ft. Then, in the equation:
d = 3.5 n + ??
↓
5ft = 3.5 · 1 + ??
↓
5 - 3.5 = ??
1.5 = ??
Then the complete equation is
d = 3.5n + 1.5
If we replace n by 1, 2, 3, 4,..., 18 we will have all the values found in the table