Question

What is the equation of the line that is parallel to y=x+4 and that passes through (5,–4)?

Answer 1

y =
`(1)/(5)` x - 5

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)/(5)` x + 4 ← is in slope- intercept form

with slope m =
`(1)/(5)`

• Parallel lines have equal slopes , then

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

to find c substitute (5, - 4 ) into the partial equation

- 4 = 1 + c ⇒ c = - 4 - 1 = - 5

y =
`(1)/(5)` x - 5 ← equation of parallel line