Find an equation of the line that is parallel to the graph of 3x+2y=6 and contains the point (6,-3).

3x + 2y = 12

Step-by-step explanation:

The equation of a line in slope- intercept form is

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

Given

3x + 2y = 6 ( subtract 3x from both sides )

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

y = - x + 3 ← in slope- intercept form

with slope m = -

Parallel lines have equal slopes , then

y = - x + c ← is the partial equation

To find c substitute (6, - 3 ) into the partial equation

- 3 = - 9 + c ⇒ c = - 3 + 9 = 6

y = - x + 6 ← in slope- intercept form

Multiply through by 2

2y = - 3x + 12 ( add 3x to both sides )

3x + 2y = 12 ← in standard form