Question 665933
Starting with the line -2x-7y=7
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Put it into slope-intercept form of y=mx+b
{{{-2x - cross(7y) + cross(7y) - highlight(7) = cross(7) + highlight(7y) - cross(7)}}}
Yielding
7y = -2x - 7
Divide both sides by 7 to isolate y
y = {{{-2x/7 - 7/7}}} which is the same as y = {{{-2/7}}}x - 1
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The slope of this line is {{{highlight(-2/7)}}}
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(The perpendicular line will need to have the slope of {{{7/2}}}, which is the negative reciprocal.)
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Using, did you mean, -9x-4y=-6, put it into y=mx+b
{{{-9x - cross(4y) + highlight(6) = cross(-6) + highlight(4y) + cross(6)}}}
Yielding
4y = -9x + 6
Divide both sides by 4 to isolate y
y = {{{(-9x/4) + (6/4)}}} which is the same as y = {{{-9/4}}}x + {{{3/2}}}
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The y intercept is {{{highlight(3/2)}}}
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(The new line will need to have the y intercept of (3/2))}}}
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Plugging in the slope of {{{7/2}}} and intercept of {{{3/2}}},
the new line will be 
{{{highlight_green(y = (7/2)x + (3/2))}}}
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Red line:  new line {{{y = (7/2)x + (3/2)}}}
Green line:  {{{y = (-2/7)x - 1}}}
Blue line: {{{y = (-9/4)x + (3/2)}}}
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{{{graph(300,200,-10,10,-10,10,(7/2)x+(3/2),(-2/7)x-1,(-9/4)x+(3/2))}}}
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