Question

Write an equation for a line that goes through (3, -7) and is parallel to the line y = 2x - 17

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{m}{\downarrow }}{2}x-17\qquad \impliedby \qquad \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}`

so we are really looking for the equation of a line whose slope is 2 and it passes through (3 , -7)

`(\stackrel{x_1}{3}~,~\stackrel{y_1}{-7})\hspace{10em} \stackrel{slope}{m} ~=~ 2 \\\\\\ \begin{array}c \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}{2}(x-\stackrel{x_1}{3}) \implies y +7 = 2 ( x -3) \\\\\\ y +7 = 2 x -6 \implies {\Large \begin{array}{llll} y = 2 x -13 \end{array}}`