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

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

## This Post Has 4 Comments

1. Expert says:

Welp life just is hard

2. zivicion says:

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

$\bf y=\stackrel{slope}{-\cfrac{1}{2}}x+3$

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

$\bf \textit{perpendicular, negative-reciprocal slope for slope}\quad -\cfrac{1}{2}\\\\&10;slope=-\cfrac{1}{{{ 2}}}\qquad negative\implies +\cfrac{1}{{{ 2}}}\qquad reciprocal\implies + \cfrac{{{ 2}}}{1}\implies 2$

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

$\bf \begin{array}{lllll}&10;&x_1&y_1\\&10;% (a,b)&10;&({{ -7}}\quad ,&{{ 2}})&10;\end{array}&10;\\\\\\&10;% slope = m&10;slope = {{ m}}= \cfrac{rise}{run} \implies 2&10;\\\\\\&10;% point-slope intercept&10;\stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-2=2[x-(-7)]&10;\\\\\\&#10;y-2=2(x+7)\implies y-2=2x+14\implies y=2x+16$

3. Expert says:

step-by-step explanation:

4. kevinmoore2884 says:

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