Question

Write an equation in slope-intercept form of the line that passes through the given point and is parallel to the graph of the given equation. (-5,-8); y=-3x+5

Answer 1

у₁=kx+b; y₂= -3x+5

y₁||y₂⇒ k= -3; y₁= -3x+b

-8 =-3*(-5)+b

-8=15+b

-23=b

y₁= -3x-23

Answer 2

a parallel line to that equation will have the same exact slope, so

$\bf y=\stackrel{\stackrel{m}{\downarrow }}{-3}x+5\impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}$

then we're really looking for the equation of a line whose slope is -3, and runs through (-5,-8)

$\bf (\stackrel{x_1}{-5}~,~\stackrel{y_1}{-8})~\hspace{10em} slope = m\implies -3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-8)=-3[x-(-5)] \\\\\\ y+8=-3(x+5)\implies y+8=-3x-15\implies y=-3x-23$