Question

Identify an equation in point-slope form for the line perpendicular to y = - 1/3 * x - 6 that passes through (- 1, 5)

A)y - 5 = 3(x + 1)
B)y - 5 = - 1/3 * (x + 1)
C)y + 5 = 1/3 * (x - 1)
D)y + 1 = 3(x - 5)

Answer 1

A

Explanation:

The equation of a line in slope- intercept form is

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

y = -
`(1)/(3)` x - 6 ← is in slope- intercept form

with slope m = -
`(1)/(3)`

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

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

The equation of a line in point- slope form is

y - b = m(x - a)

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

here m = 3 and (a, b) = (- 1, 5), thus

y - 5 = 3(x - (- 1)), that is

y - 5 = 3(x + 1) → A