Given two straight lines L1: MX + 8y + n = 0 and l: 2x + MY-1 = 0, try to determine the value of M, n 1: L1 and L2 intersect at point (m, - 1) 2: L1 is parallel L2 3: L1 is vertical L2, and the intercept of L1 on Y axis is - 1

Given two straight lines L1: MX + 8y + n = 0 and l: 2x + MY-1 = 0, try to determine the value of M, n 1: L1 and L2 intersect at point (m, - 1) 2: L1 is parallel L2 3: L1 is vertical L2, and the intercept of L1 on Y axis is - 1

(1) Because both lines pass through the point (m, - 1), we first substitute (m, - 1) into L2 to get 2m-m-1 = 0, that is, M = 1, and then substitute it into L1 to get n = 7
(2) Parallel means that the slope is the same, the slope of L1 is - M / 8, the slope of L2 is - 2 / m, make it equal, get m = + \ - 4
(3) If it is vertical, the slopes are reciprocal and the intercept of L1 is - 1, indicating that n = 8