Question

Write an equation of a line parallel to y = -5x + 1 and goes through point (6,-2).

Answer 1

keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above

`y=\stackrel{\stackrel{\textit{\small m}}{\downarrow }}{-5}x+1\qquad \impliedby \qquad \begin{array}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}`

so we are really looking for the equation of a line whose slope is -5 and it passes through (6 , -2)

`(\stackrel{x_1}{6}~,~\stackrel{y_1}{-2})\hspace{10em} \stackrel{slope}{m} ~=~ -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-\stackrel{y_1}{(-2)}=\stackrel{m}{-5}(x-\stackrel{x_1}{6}) \implies y +2 = -5 ( x -6) \\\\\\ y +2 = -5 x +30 \implies {\Large \begin{array}{llll} y = -5 x +28 \end{array}}`