Question

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

Answer 1

`y = -2/3x -2`

Because we can find the slope, and then solve for the constant by plugging in a point.

Explanation:

Perpendicular lines have opposite reciprocal slopes.

http://www.algebralab.org/lessons/lesson.aspx?file=Geometry_CoordParallelPerpendicular.xml

Above is a great explanation of why that is and some practice.

So the slope of this new line is `-2/3`. Lets start making a new equation in the form `y = mx + b`

`y = mx + b`

`y = -2/3x + b`

Now we plug in the given point `(3,-4)` to find what `b` should be

`-4 = -2*3/3 + b`

`b=-2`

So our final equation is:

`y = -2/3x -2`