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

y = x - 9

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 )

rearrange 2x - 3y = 6 into this form

subtract 2x from both sides

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

y = x - 2 ← in slope- intercept form

with m =

• Parallel lines have equal slopes, hence

y = x + c ← is the partial equation

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

- 3 = 6 + c ⇒ c = - 3 - 6 = - 9

y = x - 9 ← equation of parallel line

the translated point is (5,2)