Final answer:
The slope of the given line is 5/4. A line parallel to it would have a slope of 5/4, and a line perpendicular to it would have a slope of -4/5.
Step-by-step explanation:
The equation -5x+4y=-8 represents a straight line. To find the slope of the line, we need to rearrange the equation into slope-intercept form, which is of the form y = mx + b where m is the slope. In this case, by isolating y, the equation becomes y = (5/4)x - 2. Therefore, the slope of the line is 5/4.
A line parallel to the given line will have the same slope of 5/4, while a line perpendicular to the given line will have a slope that is the negative reciprocal of 5/4. The negative reciprocal of a number is found by flipping the fraction and changing the sign. So, the slope of a line perpendicular to -5x+4y=-8 is -4/5.