Question

Write the equation of each line in

slope-intercept form.
The line parallel to y = 5x + 1 that passes through (-1, 2).
O y = 5x + 7
O y = -1/5x+ 2
O y = -5x-1
O y = 5x + 1

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 }}{5}x+1\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}`

so we're really looking for the equation of a line whose slope is 5 and that it passes through (-1 , 2)

`(\stackrel{x_1}{-1}~,~\stackrel{y_1}{2})\hspace{10em} \stackrel{slope}{m} ~=~ 5 \\\\\\ \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}{2}=\stackrel{m}{ 5}(x-\stackrel{x_1}{(-1)}) \implies y -2= 5 (x +1) \\\\\\ y-2=5x+5\implies {\LARGE \begin{array}{llll} y=5x+7 \end{array}}`