the standard form of a line is in the form Ax + By = C where A is a positive integer, and B, and C are integers.

we have the line -9x=12y+6 and we will write it in slope-intercept form to find the slope

-9x=12y+6

12y+6 = -9x

12y = -9x - 6 divide both sides by 12

y = -(9/12)x - 6/12

y = -(3/4)x - 1/2

the slope m = -3/4 and y-intercept b= -1/2

Since parallel lines have same slopes we have the slope of the line we are looking for.

Also the line is going through a different y-intercept thus its slope-intercept equation will be

y = - (3/4)x + b1, where b1 <> -1/2

the standard form will be

y + (3/4)x = b1 multiply both sides by 4

4y + 3x = 4b1

3x + 4y = 4b1

4b1 <> -1/2

b1 <> -1/8

for example for 4b1=1 one such line is

3x + 4y = 1

Equation of a line in a standard form that is parallel to -9x=12y+6 but going through a different y-intercept is

3x + 4y = b where b<> -1/8.