Question

What is the equation of the line perpendicular to `y=-3/4x` that passes through `(2,4)`?

Answer 1

`y=4/3x+4/3`

Explanation:

We begin by finding the slope of the line that is perpendicular to `-3/4`. Recall that the perpendicular slope is expressed as the negative reciprocal of the slope(`m`) or `-1/m`.

Therefore, if the slope is `-3/4` the perpendicular slope is...

`-1/(-3/4)->-1*-4/3=4/3`

Now that we have the perpendicular slope, we can find the equation of the line by using the point-slope formula: `y-y_1=m(x-x_1)` where `m` is the slope and `(2,4)->(x_1,y_1)`

So to find the equation of the line...

`y-4=4/3(x-2)larr` Equation of the line

We can also rewrite the above equation in `y=mx+b` form if desired. To do this, we simply solve for `y`:

`y-4=4/3x-8/3`

`y-4=4/3x-8/3`

`ycancel(-4)cancelcolor(red)(+4)=4/3x-8/3color(red)(+4)`

`y=4/3x-8/3+[4/1(3/3)]`

`y=4/3x-8/3+12/3`

`y=4/3x+4/3`