Question

The equation for line A is given by Y=1/3x+4.Suppose line A is parallel to line B and line T is perpendicular to line A. Point (-3,1) lies on both line B and T

Part A: Write an equation for line B

Part B: Write an equation for line T

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 )

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

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

(a)

Parallel lines have equal slopes, thus

y =
`(1)/(3)` x + c ← is the partial equation of line B

To find c substitute (- 3, 1) into the partial equation

1 = - 1 + c ⇒ c = 1 + 1 = 2

y =
`(1)/(3)` x + 2 ← equation of line B

(b)

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

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

y = - 3x + c ← is the partial equation of line T

To find c substitute (- 3, 1) into the partial equation

1 = 9 + c ⇒ c = 1 - 9 = - 8

y = - 3x - 8 ← equation of line T