Question

Punctele A(-1;4) si B(2; -5) apartin reprezentarii grafice a funcitei F: R -> R, f(x)= ax + b. Determinati numerele a si b.

Answer 1

[tex]A(-1;4) \in G_f \longrightarrow f(-1)=4 \ \ \ ; \ \ \ f(-1)=-a+b \\\\\underline{-a+b=4} \\\\\\ B(2;-5) \in G_f \longrightarrow f(2)=-5 \ \ \ ; \ \ \ f(2)=2a+b \\\\\underline{2a+b=-5} \\\\ \hbox{Se formeaza un sistem din cele 2 ecuatii:} \\\\\\ \left \{ {{-a+b=4} \ |2\atop {2a+b=-5}} \right. \\\\\\ \underline{\left \{ {{-\not 2a+2b=8} \atop {\not 2a+b=-5}} \right. } \\ 3b=3 \\\\ \boxed{b=1} \\\\ -a+b=4 \\\\ a=b-4 \\\\ a=1-4 \\\\ \boxed{a=-3}[/tex]