Question

Write the equation parallel to the line 3y = 2x - 5 that goes through the point (6,5)

Answer 1

3y = 2x + 3

Explanation:

The equation of a line in slope- intercept form is

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

Given

3y = 2x - 5 ( divide terms by 3 )

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

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

Parallel lines have equal slopes , then

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

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

5 = 4 + c ⇒ c = 5 - 4 = 1

y =
`(2)/(3)` x + 1 ( multiply through by 3 to clear the fraction )

3y = 2x + 3 ← equation of parallel line