Question

The function f is linear. If f(2) = 2 and f(-6)=6 find f(6)

Answer 1

`The\ slope-intercept\ form:y=mx+b\\\\f(2)=2\to for\ x=2\to y=2\\f(-6)=6\to for x=-6\to y=6\\\\put\ in\ equation\ of\ the\ line:\\\\ -\left\{\begin{array}{ccc}2=2m+b\\6=-6m+b\end{array}\right\ \ \ |subtract\ sides\ of\ the\ equations\\----------\\.\ \ \ -4=8m\ \ \ \ \ |divide\ both\ sides\ by\ 8\\.\ \ \ \ \boxed{m=-(1)/(2)}\\\\put\ m=-(1)/(2)\ to\ equation\ 2=2m+b:\\\\2=2\cdot(-(1)/(2))+b\\2=-1+b\ \ \ \ |add\ 1\ to\ both\ sides\\\boxed{b=3}\\\\\boxed{\boxed{y=-(1)/(2)x+3}}`


`therefore:f(x)=-(1)/(2)x+3\Rightarrow f(6)=-(1)/(2)\cdot6+3=-3+3=0\\\\Answer:\boxed{f(6)=0}`