what is the parallel line of 6x-5y=9 containting the point (9,-3) in slope intersect form?

Question

this math class sucks and i cant figure out how to do this question

Answer 1

6x - 5y = 9
5y = 6x - 9
y = (6/5)x - (9/5)

Thus, the slope of this line is 6/5.
The slope of the parallel line will thus also be 6/5.

Using the slope formula, we have:

(y - (-3)) / (x - 9) = 6/5
(y + 3) / (x - 9) = 6/5
y + 3 = (6/5)(x - 9)
y + 3 = (6/5)x - (54/5)
y = (6/5)x - (54/5) - 3
y = (6/5)x - (69/5), which is the equation of the line you need.