The lines y = 3(x-2) and 2y = 6x -9 are parallel if they have the same slope.

Express the equation of the lines in the form y = mx + c

y = 3x - 6 and y = 3x - (9/2)

The slope in both cases is 3.

**This proves that the lines are parallel.**

The lines y = 3(x-2) and 2y = 6x -9 are parallel if they have the same slope.

Express the equation of the lines in the form y = mx + c

y = 3x - 6 and y = 3x - (9/2)

The slope in both cases is 3.

**This proves that the lines are parallel.**