[tex]\text{Ecuatia dreptei AB: }\\AB:\frac{x-x_B}{x_A-x_B}=\frac{y-y_B}{y_A-y_B}\leftrightarrow\frac{x+1}{2+1}=\frac{y-1}{-1-1}\leftrightarrow-2(x+1)=3(y-1)\\\leftrightarrow-2x-2=3y-3\leftrightarrow2x+3y-1=0\\\text{Vom nota cu }d\text{ dreapta paralel\u a la AB \c si care trece prin origine.}\\\text{Dou\u a drepte sunt paralele dac\u a au pante egale. Adic\u a: }\\m_{AB}=m_d\\
\text{Panta dreptei AB: }\\2x+3y-1=0\leftrightarrow3y=-2x+1\leftrightarrow y=-\frac{2}{3}x+\frac{1}{3}\rightarrow[/tex][tex] m_{AB}=-\frac{2}{3}=m_d\\\text{Vom afla ecua\c tia dreptei }d\text{ \c stiind un punct de pe dreapt\u a }O(0, 0)\\\text{ \c si panta acesteia, }m_d.\\d:y-y_O=m_d(x-x_O)\leftrightarrow y-0=-\frac{2}{3}(x-0)\leftrightarrow y=-\frac{2}{3}x.[/tex]
