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 $f(x) = 6-x$.