What is the equation of the line that is perpendicular to the given line and passes through the point (3, 4)?

Ok so the gradient if the given (blue) line is -1/3, as the y value decreases by a third every time you go across one unit.

To find a perpendicular line, the product of the two gradients must equal -1, so if "m" is the gradient we are trying to find;

So:

Now we can use the gradient-point formula
(y - Y) = m(x-X), with X and Y representing the new point we are given, (3,4).

So:


So:

And that is the equation we are looking for.

Hope this helped