The correct answer is C. The lines are perpendicular because the slopes, 3/2 and -2/3, are opposite reciprocals of each other.
When examining the equations of two lines, to determine the relationship between them—specifically, whether they are parallel or perpendicular—we need to look at their slopes. The slope of a line in the format ax + by = c is found by rearranging the equation into slope-intercept form, which is y = mx + b, where m represents the slope and b represents the y-intercept.
For the first equation, 3x - 2y = -5, we rearrange to get y = 3/2 x + 5/2, meaning the slope is 3/2. For the second equation, 2x + 3y = 5, rearranging yields y = -2/3 x + 5/3, which indicates a slope of -2/3. These slopes are negative reciprocals of each other, which means that the lines are indeed perpendicular. Therefore, the correct answer is C. The lines are perpendicular because the slopes are opposite reciprocals of one another.