A line passes through (1,1) , (-2,4) , and (6,n) . Find the value of n.

1 answer:

8 0

$General\ formula\ for\ line:\\y=ax+b\\\\ Passes\ through\ (1,1)\ (-2,4)\\\\\left \{ {{1=1a+b\ |\cdot2} \atop {4=-2a+b}} \right. \\\\ \left \{ {{2=2a+2b} \atop {4=-2a+b}} \right. \\+-----\\\\6=3b\ \ |:3\\b=2\\\\1=a+2\\1-2=a\\a=-1\\\\y=-x+2\\\\Passes\ through\ (6,n):\\\\n=-6+2\\\\\boxed{n=-4}$

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Vadim26 [7]

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Step-by-step explanation:

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$\frac{3-12 x^{2}-2 x}{3 x}=0$

Multiplying by 3x on both sides,

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$12 x^{2}+2 x-3=0$

Using quadratic formula, we can solve for x.

$\begin{aligned}x &=\frac{-2 \pm \sqrt{2^{2}-4 \cdot 12 \cdot(-3)}}{2 \cdot 12} \\&=\frac{-2 \pm \sqrt{4+144}}{2 \cdot 144} \\&=\frac{-2 \pm \sqrt{148}}{24} \\&=\frac{-2 \pm 2 \sqrt{37}}{24}\end{aligned}$