Question

The linear function f with values f(-6) = 8 and f(5) = 3 is f(x) =

Answer 1

You can compute the slope given that you have two points $(-6,8)$ and $(5,3)$.

$m=\frac{3-8}{5-(-6)}=\frac{-5}{11}=-\frac{5}{11}$

Your function has a form of,

$f(x)=mx+n$

So we also need to find n. To do that, substitute y and x for some point we already know, I will pick point $(5,3)$ then solve for n,

$3=-\frac{5}{11}\cdot5+n$

$n=3+\frac{5}{11}\cdot5$

$n=3+\frac{25}{11}$

$n=\frac{33+25}{11}=\frac{58}{11}$

So the function is,

$f(x)=-\frac{5}{11}x+\frac{58}{11}$

Hope this helps :)