The parallel line would have an equation of y = 3x + 3
In order to find this we need to start with the slope. The slope of a parallel line has the same slope. Since the coefficient of x (which is the slope) of the original equation is 3, we know the new slope is 3. Now we can take that and the point and put them both into slope intercept form to find the intercept.
y = mx + b
6 = 3(1) + b
6 = 3 + b
3 = b
Now that we have the slope (3) and the intercept (3), we can put them in for our final answer.
y = 3x + 3
