A line passes through (6,3), (8,4), and (n, -2). Find the value of n

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07-10-2014
Mathematics

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A line passes through (6,3), (8,4), and (n, -2). Find the value of n

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luana luana · Answer 1 · 2014-10-07T11:25:47+02:00

[tex]General\ equation\ for\ line\ in\ slope\ intercept\ form:\\y=ax+b\\\\To\ find\ a\ and\ b\ substitude\ points\ (6,3),\ (8,4)\ into\ equation\\\\ \left \{ {{3=6a+b}\ \ \ \ \atop {4=8a+b\ |*-1}} \right.\\\\ \left \{ {{3=6a+b}\ \ \ \ \atop {-4=-8a-b\}} \right.\\+----\\-1=-2a\ \ |:-2\\\\a=\frac{1}{2}\\\\3=6\cdot\frac{1}{2}+b\\3=3+b\\b=3-3=0\\y=\frac{1}{2}x\\\\To\ find\ value\ of\ n\ we\ have\ to\ substitute\ (n,-2)\ to\ equation:\\\\-2=\frac{1}{2}n\ \ \ \ \ \ \ \ \ |\cdot2\\\\n=-4[/tex]