Resposta :
Vamos lá, então. Já que você já sabe a fórmula, só vamos substituir:
a) [tex]m = \frac{\Delta y}{\Delta x} = \frac{y_{b}-y_{a}}{x_{b}-x_{a}} = \frac{-5-7}{3-1} = \frac{-12}{2} = \boxed{-6} \\\\\\ y-y_{0} = m(x-x_{0}) \\\\ y-7 = -6(x-1) \\\\ y-7 = -6x+6 \\\\ 6x+y-7-6 = 0 \\\\ \boxed{\boxed{6x+y-13 = 0}} \rightarrow \text{equa\c{c}\~{a}o geral da reta}[/tex]
b) [tex]m = \frac{\Delta y}{\Delta x} = \frac{y_{b}-y_{a}}{x_{b}-x_{a}} = \frac{-2-5}{5-(-1)} = \frac{-7}{5+1} = \boxed{-\frac{7}{6}} \\\\\\ y-y_{0} = m(x-x_{0}) \\\\ y-5 = -\frac{7}{6}(x-(-1)) \\\\ y-5 = -\frac{7}{6}(x+1) \\\\ y-5 = -\frac{7x}{6} - \frac{7}{6} \\\\ \frac{7x}{6}+y-5+\frac{7}{6} = 0 \ \ \ \times 6 \\\\ 7x+6y-30+7 = 0 \\\\ \boxed{\boxed{7x+6y-23=0}} \rightarrow \text{equa\c{c}\~{a}o geral da reta}[/tex]
c) [tex]m = \frac{\Delta y}{\Delta x} = \frac{y_{b}-y_{a}}{x_{b}-x_{a}} = \frac{-4-(-2)}{-2-(-4)} = \frac{-4+2}{-2+4} = \frac{-2}{2} = \boxed{-1} \\\\\\ y-y_{0} = m(x-x_{0}) \\\\ y-(-2) = -1(x-(-4)) \\\\ y+2 = -1(x+4) \\\\ y+2 = -x-4 \\\\ x+y+2+4=0 \\\\ \boxed{\boxed{x+y+6=0}} \rightarrow \text{equa\c{c}\~{a}o geral da reta}[/tex]
a) [tex]m = \frac{\Delta y}{\Delta x} = \frac{y_{b}-y_{a}}{x_{b}-x_{a}} = \frac{-5-7}{3-1} = \frac{-12}{2} = \boxed{-6} \\\\\\ y-y_{0} = m(x-x_{0}) \\\\ y-7 = -6(x-1) \\\\ y-7 = -6x+6 \\\\ 6x+y-7-6 = 0 \\\\ \boxed{\boxed{6x+y-13 = 0}} \rightarrow \text{equa\c{c}\~{a}o geral da reta}[/tex]
b) [tex]m = \frac{\Delta y}{\Delta x} = \frac{y_{b}-y_{a}}{x_{b}-x_{a}} = \frac{-2-5}{5-(-1)} = \frac{-7}{5+1} = \boxed{-\frac{7}{6}} \\\\\\ y-y_{0} = m(x-x_{0}) \\\\ y-5 = -\frac{7}{6}(x-(-1)) \\\\ y-5 = -\frac{7}{6}(x+1) \\\\ y-5 = -\frac{7x}{6} - \frac{7}{6} \\\\ \frac{7x}{6}+y-5+\frac{7}{6} = 0 \ \ \ \times 6 \\\\ 7x+6y-30+7 = 0 \\\\ \boxed{\boxed{7x+6y-23=0}} \rightarrow \text{equa\c{c}\~{a}o geral da reta}[/tex]
c) [tex]m = \frac{\Delta y}{\Delta x} = \frac{y_{b}-y_{a}}{x_{b}-x_{a}} = \frac{-4-(-2)}{-2-(-4)} = \frac{-4+2}{-2+4} = \frac{-2}{2} = \boxed{-1} \\\\\\ y-y_{0} = m(x-x_{0}) \\\\ y-(-2) = -1(x-(-4)) \\\\ y+2 = -1(x+4) \\\\ y+2 = -x-4 \\\\ x+y+2+4=0 \\\\ \boxed{\boxed{x+y+6=0}} \rightarrow \text{equa\c{c}\~{a}o geral da reta}[/tex]