zad. 4
[tex]y = a_{1}x + b_{1} \\ y = a_{2}x + b_{2}[/tex]
[tex]y = \frac{1}{2} x - 3 \\ a_{1} = \frac{1}{2} [/tex]
[tex]P = ( - 1,4)[/tex]
[tex]4 = - a_{2} + b \\ [/tex]
prostopadle
[tex] a_{1} \times a_{2} = - 1 \\ \frac{1}{2} \times a_{2} = - 1 \: \: \: \: | \times 2 \\ a_{2} = - 2[/tex]
[tex]4 = - ( - 2) + b \\ 4 = 2 + b \\ b = 2[/tex]
równanie prostej prostopadłej
[tex]y = - 2x + 2[/tex]
zad. 5
[tex] - \frac{5}{2} x - 10 < 0 \\ - \frac{5}{2}x < 10 \: \: \: \: \: | \div ( - \frac{5}{2} ) \\ x > 10 \times ( - \frac{2}{5} ) \\ x > - 4 \\ \\ xe( - 4; \infty )[/tex]
