Question

Suppose f is a linear function such that f(3 = 5 and f(7 = -4. find the equation for f

Answer 1

`\displaystyle\\ f(3) = 5 \\ f(7) = -4\\\\ \texttt{Solve:}\\\\ f(x)=ax+b ~~~\Longleftrightarrow~~~ y=ax+b~~~\Longleftrightarrow~~~ ax+b-y=0\\\\ -------\\ 3a+b-5=0~~~(E1)\\ 7a+b+4=0~~~(E2)\\ ---\\ E2 - E1\\ 4a+9=0\\ 4a =-9\\\\ \boxed{a = -(9)/(4) = -2,25}\\\\ 3* \Big(-(9)/(4)\Big) + b -5 = 0\\\\ -(27)/(4) -5+ b = 0\\\\ (-27-20)/(4) + b = 0\\\\ -(47)/(4) + b = 0\\\\ \boxed{b = (47)/(4) = 11,75}`