Find the equation of the line through (4,3) perpendicular to the line 3x + y = 7.
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You can easily write the equation of the line you have in this form: y= -3x +7.

Then the condition for a line to be perpendicular to a given line is that its gradient multiplied by the gradient of the given line must give - 1 as result.

The given line has gradient 3, then the gradient of the perpendicular line must be - 1/3, since 3 multiplied -1/3 is equal to -1.


To this condition you have to add the passage through the point (4;3) which is:

y - 3=-1/3 * (x-3)    which leads to

y= -x/3 + 1

and that's the equation of the perpendicular line passing through (4;3)

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