Final answer:
The distance between the parallel lines y = 2x - 1 and y = 2x + 9 is calculated using the distance between two parallel lines formula and is approximately 4.472 units.
Step-by-step explanation:
The distance between the two parallel lines y = 2x - 1 and y = 2x + 9 can be found using the formula for the distance between two parallel lines, which is |c2 - c1| / √(1 + m^2), where c1 and c2 are the y-intercepts of the lines and m is the slope.
For these lines, since both have a slope (m) of 2, we can directly plug in the intercepts (-1 and +9) into the formula, which gives us:
|9 - (-1)| / √(1 + 2^2) = 10 / √5
= 10 / √5
So, the distance between the two parallel lines is 10 / √5 units or, when simplified, 4.472 units (approximately).