Question

In equation of a line parallel to the line represented by the equation y=-1/2x-5 and passing through (6,-4) is

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 }}{-\cfrac{1}{2}}x-5\qquad \impliedby \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 for the equation of a line whose slope is -1/2 and passes through (6 , -4)

`(\stackrel{x_1}{6}~,~\stackrel{y_1}{-4})\qquad \qquad \stackrel{slope}{m}\implies -\cfrac{1}{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}{(-4)}=\stackrel{m}{-\cfrac{1}{2}}(x-\stackrel{x_1}{6}) \\\\\\ y+4=-\cfrac{1}{2}x+3\implies y=-\cfrac{1}{2}x-1`