Final answer:
The lines represented by the equations y - 5x = -5 and 4y - 20x = -20 are neither parallel nor perpendicular.
Therefore, the correct answer is d) neither parallel nor perpendicular.
Step-by-step explanation:
The lines represented by the equations y - 5x = -5 and 4y - 20x = -20 are neither parallel nor perpendicular. To determine the relationship between the lines, we can compare their slopes. The first equation, y - 5x = -5, can be rearranged to y = 5x - 5, where the slope is 5. The second equation, 4y - 20x = -20, can be rearranged to y = 5x - 5, where the slope is also 5.
Since the slopes of the two lines are equal, the lines are parallel. However, since the y-intercepts (or the values of y when x = 0) are different (-5 in the first equation and -5 in the second equation), the lines are not coincident or the same line. Therefore, the correct answer is d) neither parallel nor perpendicular.
The lines represented by the equations y - 5x = -5 and 4y - 20x = -20 can be analyzed by bringing them to slope-intercept form, y = mx + b, where m represents the slope and b the y-intercept of the line.
If we simplify the second equation by dividing every term by 4, we get y - 5x = -5, which is identical to the first equation. Since they have the same slope and the same y-intercept, they are the same line, which means they are coincident.
Therefore, the correct answer is d) neither parallel nor perpendicular.