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Explanation:
The line y = 2x-8 is in y = mx+b form with m = 2 as the slope. Anything parallel to this will have the same slope m = 2. Parallel lines always have equal slopes, but different y intercepts.
We will use m = 2 and the given point (x,y) = (-3,6) to find the y intercept b
y = mx+b
6 = 2(-3)+b
6 = -6+b
6+6 = -6+b+6
12 = b
b = 12
So y = mx+b turns into y = 2x+12
As a way to check, plug in x = -3 and we should get y = 6 as an output
y = 2x+12
y = 2*(-3)+12
y = -6+12
y = 6
So the answer is confirmed.
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You could also use the point-slope formula
m = 2 is the slope; [tex](x_1,y_1) = (-3,6)[/tex] is the point the parallel line goes through.
So,
[tex]y-y_1 = m(x-x_1)\\\\y-6 = 2(x-(-3))\\\\y-6 = 2(x+3)\\\\y-6 = 2x+6\\\\y-6+6 = 2x+6+6\\\\y = 2x+12\\\\[/tex]
and we get the same answer.