Sure, let's solve this problem step by step.
Step 1:
The first thing to recall is that parallel lines always have the same slope. Therefore, the slope of our desired line, which is to be parallel to the line given by y = -9x + 20, will also be -9.
Step 2:
With the slope of our line determined from Step 1, it's now a matter of finding our line's y-intercept (which we shall denote here as 'b'). The point (-2,3) lies on our desired line, so we can substitute these values into the general form of the equation for a line, which is y = mx + b. Here, 'm' is the slope and 'b' is the y-intercept.
So, when we substitute, we get: 3 = -9*(-2) + b
Step 3:
Now solve this equation for 'b' and you'll find that b = -15.
So, the equation for the line parallel to y = -9x + 20 and passing through the point (-2,3) is y = -9x - 15.