Final answer:
The distance between the parallel lines r and s with equations y=-3x - 5 and y=-3x + 6 is calculated using the formula for distance between parallel lines, resulting in 11 / √10 units.
Step-by-step explanation:
To find the distance between the parallel lines r and s with equations y = -3x - 5 and y = -3x + 6, respectively, we can use the formula for the distance d between two parallel lines:
d = |c2 - c1| / √(1 + m²), where m is the slope of the lines and c1 and c2 are the y-intercepts of the lines.
Since both lines have the same slope of -3, we only need to consider the difference in their y-intercepts. The y-intercept of the first line r is -5, and the y-intercept of the second line s is +6. Substituting these values into our formula gives:
d = |6 - (-5)| / √(1 + (-3)²) = 11 / √(1 + 9) = 11 / √10
The exact distance between the two parallel lines is 11 / √10 units.