Question

What is the equation in point slope form of the line that is parallel to the given line and passes through the point (4,1)?

A Y-1=-2(x-4)
B y-1=-1/2(x-4)
C y-1=1/2(x-4)
D y-1=2(x-4)

Answer 1

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

`y-1=\stackrel{\stackrel{m}{\downarrow }}{2}(x-4)\qquad \impliedby \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}`

so we're really looking for the equation of a line with a slope of 2 and that it passes through (4 , 1)

`(\stackrel{x_1}{4}~,~\stackrel{y_1}{1})\hspace{10em} \stackrel{slope}{m} ~=~ 2 \\\\\\ \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}{1}=\stackrel{m}{2}(x-\stackrel{x_1}{4})`

kinda twins.