Question

What is the equation of a line parallel to y=4/5x + 2 and passes through (1,2)

Answer 1

$\bf y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{4}{5}}x+2\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}$

keeping in mind that parallel lines have the same exact slope, thus we're really looking for a the equation of a line whose sloope is 4/5 and runs through (1,2),

$\bf (\stackrel{x_1}{1}~,~\stackrel{y_1}{2})~\hspace{10em} \stackrel{slope}{m}\implies \cfrac{4}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{\cfrac{4}{5}}(x-\stackrel{x_1}{1}) \\\\\\ y-2=\cfrac{4}{5}x-\cfrac{4}{5}\implies y=\cfrac{4}{5}x-\cfrac{4}{5}+2\implies y=\cfrac{4}{5}x+\cfrac{6}{5}$