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;
[tex]m\times \frac{ - 1}{3} = - 1[/tex]
So:
[tex]m= 3[/tex]
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:
[tex]y - 4 = 3(x - 3)[/tex]
So:
[tex]y = 3x - 5[/tex]
And that is the equation we are looking for.
Hope this helped
