ALL LINES CAN BE REPRESENTED IN THE FORM [tex]f(x) = ax+b[/tex].
We know that:
[tex]f(1) = -5 \implies a\cdot(1)+b = -5 \implies a+b = -5[/tex]
and
[tex]f(3) = -17 \implies a\cdot(3) +b = -17 \implies 3a+b = 17[/tex]
Observe that:
[tex]3a+b = 2a+a+b = 2a+(a+b)[/tex]
So:
[tex]2a+(a+b) =-17[/tex]
But we know that [tex]a+b = -5[/tex], so:
[tex]2a+(a+b) =-17[/tex]
[tex]2a+(-5) = -17[/tex]
[tex]2a = -12[/tex]
[tex]a = -6[/tex]
Since:
[tex]a+b = -5[/tex]
[tex](-6)+b = -5[/tex]
[tex]b = 1[/tex]
So the line is:
[tex]f(x) = 1-6x[/tex]
