Question

Determinati funcita liniara al carei grafic este dreapta AB in:
A(-1,5) si B(3,-11)

Answer 1

 

$\displaystyle\bf\\Functia~liniara~este~de~forma:~~~f(x)=ax+b\\\\Scriem~sistemul~de~ecuatii cu~necunoscutele~a~si~b:\\\\f(x_{_A})=y_{_A}\\f(x_{_B})=y_{_B}\\.......\\ax_{_A}+b=y_{_A}\\ax_{_B}+b=y_{_B}\\.......\\-1a+b=5\\~~~~3a+b=-11\\.......\\-a+b=5~~\Big|\times(-1)\\~~3a+b=-11\\.......\\~~a-b=-5\\3a+b=-11\\.........................~~Adunam\\4a~~~~/~=-16\\\\a=\frac{-16}{4}\\\\\boxed{\bf~a=-4}\\\\-a+b=5\\-(-4)+b=5\\4+b=5\\b=5-4\\\boxed{\bf~b=1}\\Functia~este:\\\boxed{\bf~f(x)=-4x+1}$