SOLUTION: Write the standard form of the line that passes through (5,-3) and has a slope perpendicular to 2x+7y=16.

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First step is to find the required slope value. Perpendicular lines have slopes that are negative reciprocals of each other:

The equation of the perpendicular is . Put this into slope-intercept form, , by solving for y.



, which tells us that the slope of the perpendicular to the desired line is .

Using , we now know that the slope of the desired line is .

Now we have a point, (5,-3) and a slope, , so use the point slope form of the line:

where m is the slope and (,) are the coordinates of the given point.



Now simplify to standard form:

Multiply by 2



Distribute:



Add -7x to both sides



Add -6 to both sides:

is the desired equation, though it would be a little tidier to multiply through by -1:




Hope this helps,
John