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The equation of the line passing through (1,11)  and (-4,5) can be expressed in the form x/a + y/b = 1.  Find a.

 Feb 24, 2021
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I like $y=mx+b$ form better, so I'll use that. We have:

$11=m+b, 5=-4m+b$. Subtracting, $5m=6\implies m=\frac{6}{5}$

And $b=11-m=\frac{49}{5}$.

So $y=\frac{6}{5}x+\frac{49}{5}\implies -\frac{6}{5}x+y=\frac{49}{5}\implies -6x+5y=49\implies -\frac{6}{49}x+\frac{5}{49}y=1$. So $a=\boxed{-\frac{49}{6}}$. 

 Feb 24, 2021

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