Final answer:
The equations 3x - 5y = -1 and 5x + 3y = 2 represent lines that are perpendicular to each other, as the slopes are negative reciprocals of each other, yielding a product of -1.
Step-by-step explanation:
To determine whether the lines represented by the equations 3x - 5y = -1 and 5x + 3y = 2 are parallel, perpendicular, or neither, we must find their slopes. This involves rewriting each equation in slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept.
For the first equation 3x - 5y = -1, we solve for y to get y = (3/5)x + 1/5. Here, the slope (m) is 3/5. In the second equation 5x + 3y = 2, solving for y yields y = (-5/3)x + 2/3. The slope for this line is -5/3.
To determine the relationship between the two lines, we consider slopes. If slopes are equal, the lines are parallel. If the product of the slopes is -1, the lines are perpendicular. In this case, the product of the slopes (3/5) * (-5/3) equals -1, thus the lines are perpendicular.