Question

Find the slope of the line that is parallel and perpendicular

-7x-2y=4

Answer 1

`\bf -7x-2y=4\implies -2y=7x+4\implies y=\cfrac{7x+4}{-2}\implies y=\cfrac{7x}{-2}+\cfrac{4}{-2} \\\\\\ y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{7}{2}} x-2\qquad \impliedby \begin{array}c \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} \\\\[-0.35em] ~\dotfill`

`\bf \stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{-\cfrac{7}{2}}\qquad \qquad \qquad \stackrel{reciprocal}{-\cfrac{2}{7}}\qquad \stackrel{negative~reciprocal}{\cfrac{2}{7}}}`

now, what's the slope of a line parallel to that one above? well, parallel lines have exactly the same slope.