Question 145252
The slope of 2x-9y = 4 is 2/9. Slope m = -(Cx/Cy) where Cx is the coefficient of x and Cy is the coefficient of y. It's not necessary to do the y=mx+b, just use the 2 coefficients. The value on the right, 4 in this case, only moves the line up and down, it has no effect of the slope.
Now, we're looking for a line thru (6,-8) with a slope of 2/9 (parallel lines have the same slope).
-------------------
Now use m = (y2-y1)/(x2-x1)
Passing thru a point (X,Y), it's:   y-Y = m(x-X)
y-(-8) = (2/9)(x-6)
y+8 = (2x-12)/9
9y+72 = 2x-12
9y+84 = 2x
2x - 9y = 84