Respuesta :
[tex]\bf \begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&&(~ -2 &,& 8~)
% (c,d)
&&(~ x &,& 4~)
\end{array}
\\\\\\
% slope = m
slope \implies
\cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{4-8}{x-(-2)}\implies \cfrac{4-8}{x+2}=\stackrel{given~\underline{m}}{\cfrac{4}{5}}
\\\\\\
\cfrac{-4}{x+2}=\cfrac{4}{5}\implies -20=(x+2)4\implies -20=4x+8
\\\\\\
-28=4x\implies \cfrac{-28}{4}=x\implies -7=x[/tex]
now, as far as the second one,
[tex]\bf \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~7 &,& 5~) % (c,d) &&(~ 1 &,& y~) \end{array} \\\\\\ % slope = m slope\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{y-5}{1-7}=\stackrel{given~\underline{m}}{-\cfrac{2}{3}}\implies \cfrac{y-5}{-6}=\cfrac{-2}{3} \\\\\\ 3(y-5)=12\implies 3y-15=12\implies 3y=27 \\\\\\ y=\cfrac{27}{3}\implies y=9[/tex]
now, as far as the second one,
[tex]\bf \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~7 &,& 5~) % (c,d) &&(~ 1 &,& y~) \end{array} \\\\\\ % slope = m slope\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{y-5}{1-7}=\stackrel{given~\underline{m}}{-\cfrac{2}{3}}\implies \cfrac{y-5}{-6}=\cfrac{-2}{3} \\\\\\ 3(y-5)=12\implies 3y-15=12\implies 3y=27 \\\\\\ y=\cfrac{27}{3}\implies y=9[/tex]
