Final answer:
To find the distance between the parallel lines y = -2x + 5 and y = -2x - 5, we calculate √(1 + (-2)²) times |(5) - (-5)|, resulting in √50 or approximately 7.07 units.
Step-by-step explanation:
The question involves finding the distance between two parallel lines. The equations provided seem to have a typo, but assuming the correct equations are y = -2x + 5 and y = -2x - 5, we can use the formula for the distance between two parallel lines which is d = |c2 - c1| / √(1 + m²), where m is the slope and c1 and c2 are the y-intercepts of the lines.
Both lines have the same slope m = -2. The y-intercepts differ: c1 = 5 and c2 = -5. The distance (d) between the lines is √(1 + (-2)²) times |(5) - (-5)|, which simplifies to √5 times 10, resulting in a distance of √50 or approx. 7.07 units.