Question

How do you write the slope-intercept form of the equation of the line perpendicular to the graph of `y=-3/2x-7` that passes through (3, -2)?

Answer 1

`y=2/3x-4`

Explanation:

Slope-intercept form: y=mx+b where m is the slope and b is the y-intercept

First, let's find the slope of the equation. It is perpendicular to `y=-3/2x-7`.

Perpendicular slopes are always opposite reciprocals of one another.

Opposites: positive vs. negative (-3 and 3 are opposites)

Reciprocals: numbers that multiply to 1 (`1/3` and `3` are reciprocals), flip the numerator and denominator of a number to find its reciprocal

Opposite of `-3/2` is (positive) `3/2`

Reciprocal of `-3/2` is `-2/3`

Opposite (positive) reciprocal of `-3/2` is `2/3`

So far our equation is `y=2/3x+b`. We need to find the y-intercept.

Plug in the point that lies on this equation (3, -2)

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

`-2=2+b`

`b=-4 rarr` This is the y-intercept

The equation is `y=2/3x-4`