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Write the equation of the line perpendicular to the line 2x+ 5y = 12 and passing...

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schooledmom | (Level 1) Salutatorian

Posted August 26, 2013 at 12:51 AM via web

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Write the equation of the line perpendicular to the line 2x+ 5y = 12 and passing through the point (-10,3)

Put equation in standard form

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baxthum8 | High School Teacher | (Level 3) Associate Educator

Posted August 26, 2013 at 1:01 AM (Answer #1)

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First, identify slope ofthe line `2x + 5y =12`

by solving for y.

`y = (-2/5)x + 12/5` Slope is `-2/5` so slope of a line that is perpendicular will have a slope that is the opposite reciprocal.  That makes the slope of the line equal to `5/2` .

Using point slope form of a line `y - y_(1) = m ( x -x_(1))`

where `(x_(1), y_(1))`

represents the point(-10, 3) and m represnets slope of: `(5/2)`

This gives:  `y - 3 = 5/2 (x + 10)`

Rewrite in standard form by multiplying both sides by 2, then distributing the 2 and 5 and placing in form: `ax + by = c` ` `

`2(y - 3) = 5(x + 10)`

`2y - 6 = 5x + 50`

`5x -2y = -56` is the answer in standard form.

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