Answer:
y = -(3/5)x - 6
Explanation:
Lets look for an equation of the form y=mx+b, where m is the slope and b the y-intercept(the value of y when x=0). We are given a reference line of 3x+5y = 15. Let's rearrange that into standard form:
3x+5y = 15
5y = -3x+15
y = -(3/5)x+3
This tells us that the slope of the reference line is -(3/5). Parallel lines have the same slope.
So we know the new line must use m = -(3/5) to be parallel.
This leads to:
y = -(3/5)x + b
Any value of b will still result in a parallel line. But we want OUR parallel line to go through point (-5,-3). To find a value of b that would make that happen, enter the given point into the above equation:
y = -(3/5)x + b
(-3) = -(3/5)(-5) + b for point (-5,-3)
Now solve for b:
(-3) = -(3/5)(-5) + b
(-3) = 3 + b
b = -6
The parallel line that goes through point (-5,-3) is y = -(3/5)x - 6
See the attached graph.