# Write an equation of a line passing through (2, 4), perpendicular to 10x−5y=8

Write an equation of a line passing through (2, 4), perpendicular to 10x−5y=8
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Kailee Abbott
First, convert 10x−5y=8 into the form of y=mx+b
$10x-5y=8$
$-5y=8-10x$
$y=2x-\frac{8}{5}$
The perpendicular line to $y=2x-\frac{8}{5}$ will have a slope equal to $-\frac{1}{2}$, because perpendicular lines' slopes have a product of −1.
The new line will be
$y=-\frac{1}{2}x+b$
We know that it passes through (2,4), so we can plug that into the new equation.
$4=-\frac{1}{2}\cdot 2+b$
$4=-2+b$
$b=6$
So, the new equation of the line will be
$y=-\frac{1}{2}x+5$