Final answer:
The equation of the perpendicular line is y = (-1/6)x - 7/3. The equation of the parallel line is y = 6x + 35.
Step-by-step explanation:
To find the equation of the line that is perpendicular to y = 6x - 3 and passes through the point (-5, 5), we need to determine the slope of the given line and then find the negative reciprocal to get the slope of the perpendicular line. The given line has a slope of 6, so the perpendicular line will have a slope of -1/6. Using the point-slope form y - y₁ = m(x - x₁), where (x₁, y₁) is the given point and m is the slope, we can plug in the values to find the equation. Therefore, the equation of the perpendicular line is y - 5 = (-1/6)(x + 5), which can be simplified to y = (-1/6)x - 14/6 or y = (-1/6)x - 7/3.
To find the equation of the line that is parallel to y = 6x - 3 and passes through the point (-5, 5), we can use the same slope as the given line. Therefore, the equation of the parallel line is y - 5 = 6(x + 5), which can be simplified to y = 6x + 35.