Determine whether the pair of lines is parallel, perpendicular, or neither. \[ \begin{aligned} 15 x-4 y & =12 \\ 4 x+15 y & =45\end{aligned} \]

To determine the relationship between the two lines, we first need to put them in the slope-intercept form (y = mx + b), where m represents the slope. Starting with the first equation, \( 15x - 4y = 12 \): 1. Rearrange to solve for y: \[ -4y = -15x + 12 \] \[ y = \frac{15}{4}x - 3 \] Thus, the slope of the first line (m1) is \( \frac{15}{4} \). Now for the second equation, \( 4x + 15y = 45 \): 1. Rearrange to solve for y: \[ 15y = -4x + 45 \] \[ y = -\frac{4}{15}x + 3 \] Thus, the slope of the second line (m2) is \( -\frac{4}{15} \). Next, we analyze the slopes: - Two lines are parallel if their slopes are equal. - Two lines are perpendicular if the product of their slopes is -1. Calculating the product of the slopes: \[ m1 \cdot m2 = \frac{15}{4} \cdot \left(-\frac{4}{15}\right) = -1 \] Since the product of the slopes is -1, the lines are perpendicular. Therefore, the answer is that the pair of lines is **perpendicular**.