Question

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

Answer 1

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;

`m* ( - 1)/(3) = - 1`
So:

`m= 3`
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:

`y - 4 = 3(x - 3)`

So:

`y = 3x - 5`
And that is the equation we are looking for.

Hope this helped