Question

Write an equation perpendicular/parallel to the given line through the given point. All equations should be worked until you are in slope

intercept forms.
a. PERPENDICULAR to y = 1/4x + 3 and goes through (4.1)
b. PARALLEL to y = 4x -6 and goes thorugh (6,-3)

Answer 1

see explanation

Explanation:

The equation of a line in slope- intercept form is

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

(a)

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

with slope m =
`(1)/(4)`

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

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/((1)/(4) )` = - 4, thus

y = - 4x + c ← is the partial equation

To find c substitute (4, 1) into the partial equation

1 = - 16 + c ⇒ c = 1 + 16 = 17

y = - 4x + 17 ← equation of perpendicular line

(b)

y = 4x - 6 ← is in slope- intercept form

with slope m = 4

Parallel lines have equal slopes, thus

y = 4x + c ← is the partial equation

To find c substitute (6, - 3) into the partial equation

- 3 = 24 + c ⇒ c = - 3 - 24 = - 27

y = 4x - 27 ← equation of parallel line