Question

Equation in slope intercept form for the line parallel to y= 4x-1 containing (-3,2).

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{m}{\downarrow }}{4}x-1\qquad \impliedby \qquad \begin{array} \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 fo the equation of a line whose slope is 4 and it passes through (-3 , 2)

`(\stackrel{x_1}{-3}~,~\stackrel{y_1}{2})\hspace{10em} \stackrel{slope}{m} ~=~ 4 \\\\\\ \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}{ 4}(x-\stackrel{x_1}{(-3)}) \implies y -2= 4 (x +3) \\\\\\ y-2=4x+12\implies {\Large \begin{array}{llll} y=4x+14 \end{array}}`