EXPLANATION
Since we have the expression y= (2/3)x + 1 and we need a parallel line passing through (-6,-1), we can asseverate that the new line will have the same slope but a different y-intercept.
Therefore, we have the new expression for the parallel line:
y=(2/3)x + b
Now, in order to get the value of b we can plug the point (-6,-1) as follows:
-1 = (2/3)(-6) + b
Multiplying numbers:
-1 = (-12/3) + b
Simplifying:
-1 = -4 + b
Adding +4 to both sides:
-1 + 4 = b
Adding numbers:
3 = b
The new value of the y-intercept is b=3, plugin in this value into y=(2/3)x + b give us the following expression:
y=(2/3)x + 3