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

assupecoitteem81
2022-11-21
Answered

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

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Kailee Abbott

Answered 2022-11-22
Author has **14** answers

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

$y=-\frac{1}{2}x+5$

$10x-5y=8$

$-5y=8-10x$

$y=2x-\frac{8}{5}$

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

$y=-\frac{1}{2}x+5$

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