## Algebra 1

The two lines are parallel when $k=-1.5 (or -3/2)$. The two lines are perpendicular when $k = 24$.
$12y = -3x+8$ and $6y = kx -5$ $12y = -3x+8$ $12y/12 = (-3x+8)/12$ $y = -1/4*x + 2/3$ $6y = kx-5$ $6y/6 = (kx-5)/6$ $y = k/6*x - 5/6$ $y = 1/6*k*x - 5/6$ Parallel $-1/4 = 1/6 * k$ $24*(-1/4) = 24*(1/6*k)$ $-6 = 4k$ $-6/4 = 4k/4$ $-3/2 = k$ Perpendicular $-1/4 * (1/6 * k) = -1$ $-1/24 * k = -1$ $-24 * -1/24 * k = -1 * -24$ $k = 24$ $y = 1/6 * k * x -5/6$ $y = 1/6 * 24 *x-5/6$ $y = 4x-5/6$