Question

Find an equation of the line that satisfies the given conditions.Passes through (3,7)(3,7); parallel to the line passing through (4,5)(4,5) and (0,1)(0,1).

Answer 1

keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the line parallel to it

`(\stackrel{x_1}{4}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{1}-\stackrel{y1}{5}}}{\underset{\textit{\large run}} {\underset{x_2}{0}-\underset{x_1}{4}}} \implies \cfrac{ -4 }{ -4 } \implies 1`

so we're really looking for the equation of a line whose slope is 1 and it passes through (3 , 7)

`(\stackrel{x_1}{3}~,~\stackrel{y_1}{7})\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}{7}=\stackrel{m}{ 1}(x-\stackrel{x_1}{3}) \\\\\\ y-7=x-3\implies {\Large \begin{array}{llll} y=x+4 \end{array}}`