Final answer:
The distance between the two parallel lines y = 3x + 12 and y = 3x - 18 is 9.49.
Step-by-step explanation:
To find the distance between two parallel lines, we need to find the perpendicular distance between them. The distance between two parallel lines with equations y = mx + b1 and y = mx + b2 is given by the formula:
d = |b2 - b1| / sqrt(1 + m^2)
In this case, the equations are y = 3x + 12 and y = 3x - 18. The slopes (m) are equal, so we can use either equation for calculating the distance.
Using the formula: d = |(-18) - 12| / sqrt(1 + 3^2) = 30 / sqrt(10) = 9.49.