Question

Determine the equation of the line passing through the point below having the corresponding slope. Point: ( − 18 , − 45 ) What’s the slope of the line that passes through 5,10 and 7,12

Answer 1

`(\stackrel{x_1}{5}~,~\stackrel{y_1}{10})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{12}) ~\hfill~ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{12}-\stackrel{y1}{10}}}{\underset{\textit{\large run}} {\underset{x_2}{7}-\underset{x_1}{5}}} \implies \cfrac{ 2 }{ 2 } \implies 1`

so we are really looking for the equation of a line whose slope is 1 and it passes through (-18 , -45)

`(\stackrel{x_1}{-18}~,~\stackrel{y_1}{-45})\hspace{10em} \stackrel{slope}{m} ~=~ 1 \\\\\\ \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}{(-45)}=\stackrel{m}{1}(x-\stackrel{x_1}{(-18)}) \implies y +45 = 1 ( x +18) \\\\\\ y +45 = x +18 \implies {\Large \begin{array}{llll} y = x -27 \end{array}}`