This Post Has 4 Comments

1. Welp life just is hard

   Reply

2. First off, what is the slope of say y = -1/2x+3?  well, let's take a peek

   [tex]\bf y=\stackrel{slope}{-\cfrac{1}{2}}x+3[/tex]

   well, then, a line perpendicular to that line, will have a slope that is negative reciprocal to that one, so if the slope of that graph is -1/2, then

   [tex]\bf \textit{perpendicular, negative-reciprocal slope for slope}\quad -\cfrac{1}{2}\\\\
slope=-\cfrac{1}{{{ 2}}}\qquad negative\implies +\cfrac{1}{{{ 2}}}\qquad reciprocal\implies + \cfrac{{{ 2}}}{1}\implies 2[/tex]

   so, we're really looking for the equation of a line whose slope is 2, and runs through -7, 2.

   [tex]\bf \begin{array}{lllll}
&x_1&y_1\\
% (a,b)
&({{ -7}}\quad ,&{{ 2}})
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies 2
\\\\\\
% point-slope intercept
\stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-2=2[x-(-7)]
\\\\\\
y-2=2(x+7)\implies y-2=2x+14\implies y=2x+16[/tex]

   Reply

3. answer: a

   step-by-step explanation:

   Reply

4. A perpendicular line will have a negative reciprocal slope (-1/2 → 2/1)
   Use the given point to find the y-intercept "b" in y = mx+b

   y = 2x + b
   2 = 2(-7) + b
   2 = -14 + b
   2 + 14 = b
   16 = b

   final equation :
   y = 2x + 16

   Reply