Question

what is the equation of the line that passes through the point (-1,0) and is parallel to the line 5x-y=6

Answer 1

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

`5x-y=6\implies 5x=6+y\implies \stackrel{\stackrel{m}{\downarrow }}{5}x-6=y\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}`

so we are really looking for the equation of a line whose slope is 5 and it passes through (-1 , 0)

`(\stackrel{x_1}{-1}~,~\stackrel{y_1}{0})\hspace{10em} \stackrel{slope}{m} ~=~ 5 \\\\\\ \begin{array} \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}{0}=\stackrel{m}{5}(x-\stackrel{x_1}{(-1)}) \implies y -0 = 5 ( x +1) \\\\\\ y -0 = 5 x +5 \implies {\Large \begin{array}{llll} y = 5 x +5 \end{array}}`