Hello, Emmanuel,
I'll rewrite the equation 6x-y==1 as y=6x-1. If you meant to write 6x-y=-1, the same steps apply, but change the sign on the "1."
y=6x-1
This is in the standard form of a linear equation, y=mx+b,
where m is the slope and b is the y-intercept.
S parallel line will have the same slope, 6 in this case. So the new line can be written as y=6x+b. The value of b is what separates it from the original line. We are given one point on the new line, (-1,-3), so we can use those values of (x,y) to find b.
-3 = 6*(-1)+b
b=3
So the parallel line that goes through (-1,-3) is
y=6x+3
Bob
