Question

Write an equation of the line that passes through the point (6, 3) and is perpendicular to y=-1/3x+ 12.

y=3x+12
y=x+5
y=-1/3x+5
y=-1/3x+12

Answer 1

A:
`y=3x+12`

Explanation:

To start we need to know what makes lines perpendicular. Two perpendicular lines will have opposite-reciprocal slopes, because we know that they intersect at a right angle.

Then, we need to understand the slope-intercept form of an equation. The slope intercept form is
`y=mx+b` where
`m` is the slope of the line and
`b` is the y-intercept. We also know that
`x` and
`y` represent points on the line.

Now, since our equation is already in the correct form, we can start with finding the opposite reciprocal of the slope. To do this, all we have to do is flip the fraction upside down and multiply by -1. This means that the opposite reciprocal of
`-(1)/(3)` would be
`(3)/(1)` which can be written as
`3`.

Now, since we have a list of options and only one has the correct slope, we can safely choose option A.