Question 664512
A perpendicular line has a negative reciprocal slope.
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Starting with x+2y=6, convert it into the linear equation format
x+2y=6
2y = -x+6
y = {{{-1/2}}}x + {{{6/2}}} which is the same as y = {{{-1/2}}}x + 3
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The slope of the lines is {{{-1/2}}}.
A perpendicular line will have a slope of {{{(-1)/(-1/2)}}}
Where dividing is the same as multiplying the inverse,
{{{(-1)/(-1/2)}}} is the same as {{{-1*(-2/1)}}} = 2
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More easily, the negative inverse of {{{-1/2)}}} is {{{(2/1) = 2}}}
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Knowing the slope of 2 and using the coordinates (8, 3), solve for y-intercept, b.
3 = 2(8) + b
b = 3 - 16 = -13
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The equation of the perpendicular line that passes through (8, 3) is 
y = 2x - 13 :slope-intercept from
2x - y - 13 = 0 :standard form
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Red line: y = {{{-1/2}}}x + 3
Green line: y = 2x - 13
{{{graph(300,200,-2,10,-20,10, (-1/2)x+3, 2x-13)}}}
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