Question

Please help i’m very confused and i’ve been doing this for 2 hours

Answer 1

parallel lines have the same exact slope.... hmmm so what the slope of that equation there? low and behold, the equation is already in slope-intercept form, meaning

`\bf \begin{array}c \cline{1-1} \textit{slope-intercept form}\\ \cline{1-1} \\ y=\stackrel{\stackrel{slope}{\downarrow }}{m}x+b\\ \\\\ \cline{1-1} \end{array}~\hspace{10em}y=\stackrel{slope}{\cfrac{1}{5}}x-6`

so a parallel line to that one, will also have a slope of 1/5, so we're really looking for the equation of a line whose slope is 1/5 and runs through 1,6.

`\bf (\stackrel{x_1}{1}~,~\stackrel{y_1}{6})~\hspace{10em} slope = m\implies \cfrac{1}{5} \\\\\\ \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-6=\cfrac{1}{5}(x-1)\implies y-6=\cfrac{1}{5}x-\cfrac{1}{5} \\\\\\ y=\cfrac{1}{5}x-\cfrac{1}{5}+6\implies y=\cfrac{1}{5}x+\cfrac{29}{5}`