Answer:
To find the equation of a line parallel to 2x - 5y = 8, we need to determine the slope of the given line. By rearranging the equation into slope-intercept form (y = mx + b), we can see that the slope of the given line is 2/5.
Since parallel lines have the same slope, the line through (-4,-5) will also have a slope of 2/5. Using the point-slope form (y - y1 = m(x - x1)), we can plug in the values (-4,-5) and the slope (2/5) to find the equation of the line.
For the line perpendicular to y = -2x + 7, we can determine the slope of the given line by comparing it to the slope-intercept form (y = mx + b). In this case, the slope is -2.
Since perpendicular lines have slopes that are negative reciprocals of each other, the line through (-3,7) will have a slope of 1/2 (the negative reciprocal of -2). Using the point-slope form, we can plug in the values (-3,7) and the slope (1/2) to find the equation of the line.