Question

Find the equation of the line which passes through (6,2) and is parallel to the line with equation 3y=5x+2

Answer 1

3y = 5x - 24

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 = 5x + 2 ( divide through by 3 )

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

with slope m =
`(5)/(3)`

• Parallel lines have equal slopes , then

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

to find c substitute (6, 2 ) into the partial equation

2 = 10 + c ⇒ c = 2 - 10 = - 8

y =
`(5)/(3)` x - 8 ← equation in slope- intercept form

multiply through by 3 to clear the fraction

3y = 5x - 24 ← equation of parallel line