Question

What equation represents the line that passes through points (1.-5) and (3 -17)?

Answer 1

ALL LINES CAN BE REPRESENTED IN THE FORM
`f(x) = ax+b`.

We know that:

`f(1) = -5 \implies a\cdot(1)+b = -5 \implies a+b = -5`

and

`f(3) = -17 \implies a\cdot(3) +b = -17 \implies 3a+b = 17`

Observe that:

`3a+b = 2a+a+b = 2a+(a+b)`

So:

`2a+(a+b) =-17`

But we know that
`a+b = -5`, so:

`2a+(a+b) =-17`

`2a+(-5) = -17`

`2a = -12`

`a = -6`

Since:

`a+b = -5`

`(-6)+b = -5`

`b = 1`

So the line is:

`f(x) = 1-6x`