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

y = x - 5

Step-by-step explanation:

The equation of a line in slope- intercept form is

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

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

with slope m =

Parallel lines have equal slopes, thus

y = x + c ← is the partial equation

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

- 4 = 1 + c ⇒ c = - 4 - 1 = - 5

y = x - 5 ← equation of parallel line