What is the equation for a line that passes through (-7, 2) and is perpendicular to the graph of y=-1/2x+3

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What is the equation for a line that passes through (-7, 2) and is perpendicular to the graph of y=-1/2x+3

Welp life just is hard

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]

answer: a

step-by-step explanation:

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