Question

What is the equation of the line that passes through (4, 2) and is parallel to 3x – 2y = -6?

Answer 1

y =
`(3)/(2)` x - 4

Explanation:

The equation of a line in slope- intercept form is

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

Rearrange 3x - 2y = - 6 into this form

Subtract 3x from both sides

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

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

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

• Parallel lines have equal slopes, hence

y =
`(3)/(2)` x + c ← partial equation of parallel line

To find c substitute (4, 2) into the partial equation

2 = 6 + c ⇒ c = 2 - 6 = - 4

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