Question

What is the equation of the line that is parallel to the line y =1/3 x + 4 and passes through the point (6, 5)?

Answer 1

y =
`(1)/(3)` x + 3

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

Parallel lines have equal slopes , then

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

To find c substitute (6, 5) into the partial equation

5 = 2 + c ⇒ c = 5 - 2 = 3

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