Question

A line passes through the points (-3, -1) and (-5, 4). what is the equation of this line?

Answer 1

`(\stackrel{x_1}{-3}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{-5}~,~\stackrel{y_2}{4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{4}-\stackrel{y1}{(-1)}}}{\underset{\textit{\large run}} {\underset{x_2}{-5}-\underset{x_1}{(-3)}}} \implies \cfrac{4 +1}{-5 +3} \implies \cfrac{ 5 }{ -2 } \implies - \cfrac{ 5 }{ 2 }`

`\begin{array}ll \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}{(-1)}=\stackrel{m}{- \cfrac{ 5 }{ 2 }}(x-\stackrel{x_1}{(-3)}) \implies y +1 = - \cfrac{ 5 }{ 2 } ( x +3) \\\\\\ y+1=- \cfrac{ 5 }{ 2 }x-\cfrac{15}{2}\implies y=- \cfrac{ 5 }{ 2 }x-\cfrac{15}{2}-1\implies {\Large \begin{array}{llll} y=- \cfrac{ 5 }{ 2 }x-\cfrac{17}{2} \end{array}}`