Question

What is the equation of a line that passes through the point (9, -3) and is parallel to the line whose equation is 2x - 3y = 6 ?

PLEASE HELP

Answer 1

y =
`(2)/(3)` x - 9

Explanation:

The equation of a line in slope- intercept form is

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

Rearrange 2x - 3y = 6 into this form

Subtract 2x from both sides

- 3y = - 2x + 6 ( divide all terms by - 3 )

y =
`(2)/(3)` x - 2 ← in slope- intercept form

with m =
`(2)/(3)`

Parallel lines have equal slopes, thus

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

To find c substitute (9, - 3) into the partial equation

- 3 = 6 + c ⇒ c = - 3 - 6 = - 9

y =
`(2)/(3)` x - 9 ← equation of line