Final answer:
The lines represented by the equations 4x + y = 0 and 9x - 10 = 2y are neither parallel nor perpendicular since their slopes, -4 and 4.5 respectively, are not equal (not parallel) and not negative reciprocals of each other (not perpendicular).
Step-by-step explanation:
To decide whether the pair of lines 4x + y = 0 and 9x - 10 = 2y are parallel, perpendicular, or neither, we need to compare their slopes. The slope-intercept form of a line is y = mx + b, where m represents the slope of the line.
First, let's put both equations in the slope-intercept form:
- For 4x + y = 0, subtracting 4x from both sides gives us y = -4x + 0. Thus, the slope (m) is -4.
- For 9x - 10 = 2y, first add 10 to both sides to get 2y = 9x + 10, and then divide each term by 2, yielding y = 4.5x + 5. So, the slope (m) for this line is 4.5.
Since the slopes of the two lines are different, and neither is a negative reciprocal of the other, the lines are neither parallel nor perpendicular.
Therefore, the correct answer is:
c) Neither