determine an equation for the line perpendicular to -4x+7y=18 and passing through the point (-10,7) an equation for the perpendicular line is y=

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embizze | High School Teacher | (Level 1) Educator Emeritus

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If the line is perpendicular to -4x+7y=18 then its slope is the opposite reciprocal of the slope of the given line (the product of the slopes will be -1): The slope of -4x+7y=18 is `m=4/7` (The slope of a line given in standard form `Ax+By=C` is `m=-A/B` ; or you could rewrite in slope-intercept form to find the slope.) So the slope of teh required line is `m=-7/4` .

The required line contains the point (-10,7). Its slope is `m=-7/4` . We can use the point-slope form to get the equation:

`y-7=-7/4(x+10)==>y-7=-7/4x-35/2`

or `y=-7/4x-21/2`

 

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Then `4y=-7x-42` so the required equation is `7x+4y=-42` or in slope-intercept form `y=-7/4x-21/2`

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