Question

What is an equation in point- slope form for the line perpendicular to y= 3x-4 that contains (7,2)?

Answer 1

y - 2 = -
`(1)/(3)` (x - 7)

Explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 3x - 4 ← is in slope- intercept form

with slope m = 3

Given a line with slope m then the slope of a line perpendicular to it is

`(m)/(perpendicular)` = -
`(1)/(m)` = -
`(1)/(3)`

The equation of a line in point- slope form is

y - b = m(x - a)

m is the slope and (a, b) a point on the line

Here m = -
`(1)/(3)` and (a, b) = (7, 2), thus

y - 2 = -
`(1)/(3)`(x - 7) ← equation of perpendicular line