Question

Parallel to x-2y=17 through (-10,4)

Answer 1

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

`x-2y=17\implies -2y=-x+17\implies y=\cfrac{-x+17}{-2} \\\\\\ y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{1}{2}} x-\cfrac{17}{2}\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 that it passes through (-10 , 4)

`(\stackrel{x_1}{-10}~,~\stackrel{y_1}{4})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{2} \\\\\\ \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}\implies y-\stackrel{y_1}{4}=\stackrel{m}{ \cfrac{1}{2}}(x-\stackrel{x_1}{(-10)}) \implies y -4= \cfrac{1}{2} (x +10) \\\\\\ y-4=\cfrac{1}{2}x+5\implies {\Large \begin{array}{llll} y=\cfrac{1}{2}x+9 \end{array}}`