document.write( "Question 742132: The coordinates of 3 of the vertices of a parallelogram are (–3, 4), (–2, 1), and (2, 6). What is the equation for the line containing the side opposite the side containing the first two vertices? \n" ); document.write( "

Algebra.Com's Answer #452345 by KMST(5328) $\"\"$ $\"About$

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The slope of the line connecting (-3,4) and (-2,1) can be calculated as the difference of the y-coordinates divided by the difference of the x coordinates.
\n" ); document.write( "Subtracting the coordinates of (-3,4) minus the coordinates of (-2,1), we get
\n" ); document.write( " $\"slope=m=%284-1%29%2F%28-3-%28-2%29%29=3%2F%28-3%2B2%29=3%2F%28-1%29=-3\"$
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\n" ); document.write( "The opposite side is parallel, and parallel lines have the same slope, so the line we want also has slope $\"m=-3\"$ .
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\n" ); document.write( "The equation of a line with slope $\"-3\"$ and passing through point (2,6) can be written in point-slope form as
\n" ); document.write( " $\"y-6=-3%28x-2%29\"$
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\n" ); document.write( "The more traditional (and unique) slope-intercept form of the equation can be derived from the point-slope form above.
\n" ); document.write( " $\"y-6=-3%28x-2%29\"$ --> $\"y-6=-3x-3%2A%28-2%29\"$ --> $\"y-6=-3x%2B6\"$ --> $\"highlight%28y=-3x%2B12%29\"$ \n" ); document.write( "

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