Question

Line p has an equation of y=8/3x+2. Line q, which is parallel to p, includes the point (-2,-5). What is the equation of line q?

Answer 1

y =
`(8)/(3)` x +
`(1)/(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 =
`(8)/(3)` x + 2 ← is in slope- intercept form

with slope m =
`(8)/(3)`

Parallel lines have equal slopes , thus

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

To find c substitute (- 2, - 5) into the partial equation

- 5 = -
`(16)/(3)` + c ⇒ c = - 5 +
`(16)/(3)` =
`(1)/(3)`

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