Question

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

Answer 1

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