Final answer:
To determine the equations of the lines perpendicular and parallel to y = -3/5x - 7 passing through (-5, 2), find the reciprocal slope for the perpendicular line (5/3) and use the same slope for the parallel line (-3/5), resulting in y = 5/3x + 17/3 and y = -3/5x + 1 respectively.
Step-by-step explanation:
To find the equation of the line perpendicular to the given line y = -3/5x - 7 that passes through the point (-5, 2), we first need to find the perpendicular slope. For lines to be perpendicular, their slopes must be negative reciprocals of each other. The original slope is -3/5, so the perpendicular slope is 5/3. We use the point-slope form y - y1 = m(x - x1), where (x1, y1) is the point (-5, 2) and m is the slope 5/3:
y - 2 = 5/3(x + 5)
To find the equation of the line parallel to the given line that passes through the same point, we use the original slope of -3/5, since parallel lines have identical slopes. Using the point-slope form again, we get:
y - 2 = -3/5(x + 5)
We can then simplify both equations to their slope-intercept form, y = mx + b.
The perpendicular line equation after simplifying becomes y = 5/3x + 17/3, and the parallel line equation simplifies to y = -3/5x + 1.