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

Convert to slope intercept form to find the slope of the given line:-

2x - 3y = 6

-3y = -2x + 6

y = 2/3x - 2   The slope  = 2/3

Now we find the required equation  using the point-slope form

y - y1 = m(x - x1)

m = slope = 2/3 and (x1. y1) = (9, -3):-

y - (-3) = 2/3 (x - 9)

y = 2/3x - 6 - 3

y = 2/3x - 9  

In standard form  this is

2x - 3y =  27 answer

Hope this helps.