Question

Write the equation of the line that passes through the points

(

−

3

,

−

8

)

(−3,−8) and

(

6

,

−

4

)

(6,−4). Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal line

Answer 1

`(\stackrel{x_1}{-3}~,~\stackrel{y_1}{-8})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{-4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-4}-\stackrel{y1}{(-8)}}}{\underset{\textit{\large run}} {\underset{x_2}{6}-\underset{x_1}{(-3)}}} \implies \cfrac{-4 +8}{6 +3} \implies \cfrac{ 4 }{ 9 }`

`\begin{array}c \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-8)}=\stackrel{m}{ \cfrac{ 4 }{ 9 }}(x-\stackrel{x_1}{(-3)}) \implies y +8 = \cfrac{ 4 }{ 9 } ( x +3)`