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Find the slope‐intercept equation of the line with the following...

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ms718 | Student | eNoter

Posted September 7, 2012 at 10:59 PM via web

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Find the slope‐intercept equation of the line with the following properties:Perpendicular to the line x-4y=2; containing the point (5,2).

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lfryerda | High School Teacher | (Level 2) Educator

Posted September 8, 2012 at 1:19 AM (Answer #1)

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The slope-intercept form of a line is written as `y=mx+b` where m is the slope and b is the y-intercept.  To find this equation, we need the slope of the line and any point on the line.  We have the point, it is (5,2).  The slope is perpendicular to the line:

 `x-4y=2`  rearrange

`-4y=-x+2`   divide by -4

`y=1/4 x-2/4`   

which has slope `1/4` .  A line perpendicular to this one has a slope that is the negative reciprocal, which has slope -4.

This means the line we are looking for has slope -4 and goes through the point (5,2).

Sub into the equation of the line:

`y=mx+b`

`2=-4(5)+b`   solve for b

`2+20=b`

`b=22`

This means the equation of the line is `y=-4x+22` .

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ms718 | Student | eNoter

Posted September 8, 2012 at 5:38 AM (Answer #2)

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Thanks so very much I understand

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