Question

Find the equation of the line that passes through both (5,1) and (8,-2)

Answer 1

Let
`f(x) = ax+b` be the line that passes through both points.

We know that
`f(5) = 1` and
`f(8) = -2`. So:

`\begin{cases}5a+b = 1 \\ 8a+b = -2\end{cases}`

Solving the system, we get that a= -1 and b = 6.

So the line is equal to
`f(x) = 6-x`.