Question

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

Answer 1

`y=2/3x-16/3`

Explanation:

The slope-intercept form of a line is written in the form:

`y=mx+b`

where:
`y=`y-coordinate
`m=`slope
`x=`x-coordinate
`b=`y-intercept

Start by finding the slope that is perpendicular to `-3/2x`. Recall that when a line is perpendicular to another line, it is `90^@` to it.

We can find the slope of the line perpendicular to `-3/2x` by finding the negative reciprocal. Recall that the reciprocal of any number is `1/"number"`. In this case, it is `1/"slope"`. To find the negative reciprocal we can do:

`-(1/"slope")`
`=-(1/(-3/2x))`
`=-(1-:-3/2x)`
`=-(1*-2/3x)`
`=-(-2/3x)`
`=2/3xrArr` negative reciprocal, perpendicular to `-3/2x`

So far, our equation is: `y=2/3x+b`

Since we do not know the value of `b` yet, this is going to be what we are trying to solve for. We can do this by substituting the point, `(2,-4)`, into the equation:

`y=mx+b`
`-4=2/3(2)+b`
`-4=4/3+b`
`-16/3=b`

Now that you know all your values, rewrite the equation in slope-intercept form:

`y=2/3x-16/3`