Question

Find the missing coordinate using the given slope (-4,-10) and (-2,p) slope 5/2

Answer 1

`(\stackrel{x_1}{-4}~,~\stackrel{y_1}{-10})\qquad (\stackrel{x_2}{-2}~,~\stackrel{y_2}{p}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{p}-\stackrel{y1}{(-10)}}}{\underset{\textit{\large run}} {\underset{x_2}{-2}-\underset{x_1}{(-4)}}} ~~ = ~~\stackrel{\stackrel{\textit{\small slope}}{\downarrow }}{ \cfrac{ 5 }{ 2 }}\implies \cfrac{p+10}{-2+4}=\cfrac{ 5 }{ 2 }\implies \cfrac{p+10}{2}=\cfrac{ 5 }{ 2 }`

`2p+20=10\implies 2p=-10\implies p=\cfrac{-10}{2}\implies \boxed{p=-5}`