Question

If a straight line y = mx + c passes through the intersecting point of 3x - y = 8 and x+ 2y = 5 which is perpendicular to the line 3x + 6y - 11 = 0. Find the value of 'm' and 'c'.​

Answer 1

Point of intersection:

`3x - y = 8 - - - (a) \\ x + 2y = 5 - - - (b)`

2 × equation(b) + equation (a):

`7x = 21 \\ x = 3 \\ \\ y = 3x - 8 \\ y = 1`

Point of intersection = (3, 1)

Perpendicular line:

`3x + 6y - 11 = 0 \\ 6y = - 3x + 11 \\ y = - (1)/(2) x + (11)/(6)`

General equation of line:

`y = mx + c \\ 1 = (2 * 3) + c \\ c = - 5`

Value of m:

`m * m {}^(i) = - 1 \\ m * - (1)/(2) = - 1 \\ m = 2`