Question

Write a linear equation to describe the number pattern that starts with 3 and continues with positive odd integers.

Answer 1

In order to have a linear equation, you have to write an equation like

`y=mx+q`

The sequence has to start with 3, so we must choose
`q=3`, because this guarantees that when
`x=0` we have

`y=0\cdot m + 3 =3`

Now,
`m` must be even. In fact, if
`m` is even,
`mx` will always be even for every possible
`x`, and
`mx+3` will be odd.

So, for example, you might choose

`y=2x+3`

Which will produce the following sequence:

`\begin{array}cx&f(x)\\0&3\\1&5\\2&7\\3&9\end{array}`

and so on