Question

Determinati functia liniara al carei grafic contine punctele A(1,4) si B(-3,-6).

Answer 1

 

$\displaystyle\\\text{Functia este:}\\f(x)=ax+b\\\text{Vom scrie functia in forma:}\\\boxed{y=ax+b}\\\\\text{Vom face un sistem de ecuatii cu necunoscutele a si b}\\\\\text{x va prelua coordonata x a punctului A respectiv B.}\\\text{y va prelua coordonata y a punctului A respectiv B.}$

$\displaystyle\\\text{Rezolvare:}\\\\\begin{cases}y_{_A}=ax_{_A}+b\\y_{_B}=ax_{_B}+b\end{cases}\\\\\begin{cases}4=a\cdot1+b\\-6=a\cdot(-3)+b\end{cases}\\\\\begin{cases}a+b=4\\-3a+b=-6~~~\Big|\cdot(-1)\end{cases}\\\\\begin{cases}a+b=4\\3a-b=6\end{cases}\\...........................\text{Adunam ecuatiile}\\~~~4a~~~/~=10\\\\4a=10\\\\a=\frac{10}{4}\\ \boxed{a=2,5}\\2,5+b=4\\b=4-2,\!5\\\boxed{b=1,\!5}\\\\\text{Functia este:}\\\\\boxed{f(x)=2,\!5x+1,\!5}$