Question

Find an equation of the line passing through the point (−6,−5) that is parallel to the line y=4/3x−5

Answer 1

y =
`(4)/(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 =
`(4)/(3)` x - 5 ← is in slope- intercept form

with slope m =
`(4)/(3)`

Parallel lines have equal slopes, thus

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

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

- 5 = - 8 + c ⇒ c = - 5 + 8 = 3

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