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

Answer:

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:

$3x + 6y - 11 = 0 \\ 6y = - 3x + 11 \\ y = - \frac{1}{2} x + \frac{11}{6}$

General equation of line:

$y = mx + c \\ 1 = (2 \times 3) + c \\ c = - 5$

Value of m:

$m \times m {}^{i} = - 1 \\ m \times - \frac{1}{2} = - 1 \\ m = 2$