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:

$f(x) = 1-6x$