5. Wyznacz wzór funkcji liniowej f,która spełnia podane warunki. przykłady a) i b)

y=ax+b [latex] left { {{-4=-2a+b} atop {-1=4a+b}} ight. \ - ----\ -4-(-1)=-2a-4a\ -3=-6a /:(-6)\ a=frac{1}{2}\ \ -1=4*(frac{1}{2})+b\ -1=2+b\ b=-3\ \ oxed{y=frac{1}{2}x-3}[/latex] [latex] left { {{2=-3a+b} atop {6=3a+b}} ight. \ - ----\ 2-6=-3a-3a\ -4=-6a /:(-6)\ a=frac{2}{3}\ \ 6=3*(frac{2}{3})+b\ 6=2+b\ b=4\ \ oxed{y=frac{2}{3}x+4}[/latex] [latex] left { {{6=-8a+b} atop {4=-3a+b}} ight. \ - ----\ 6-4=-8a-(-3a)\ 2=-5a /:(-5)\ a=-frac{2}{5}\ \ 4=-3*(-frac{2}{5})+b\ 4=frac{6}{5}+b\ b=2frac{4}{5}\ \ oxed{y=-frac{2}{5}x+2frac{4}{5}}[/latex] [latex] left { {{0=0a+b} atop {2=sqrt{2}a+b}} ight. \ left { {{b=0} atop {2=sqrt{2}a+b} ight. \\ 2=sqrt{2}a /:sqrt{2}\ a=frac{2}{sqrt{2}}*frac{sqrt{2}}{sqrt{2}}=frac{2sqrt{2}}{2}=sqrt{2}\ \ oxed{y=sqrt{2}x}[/latex]