Question

A line passing through the origin perpendicularly cuts the line 3x - 2y = 6 at point m. Find m?

Answer 1

Answer:

Step-by-step explanation:A line passing through the origin perpendicularly cuts the line 2x + 3y =6 at point M. What is M?

The line 2x + 3y =6 can be written as

3y = -2x + 6, or

y = (-2/3)x + 2 …(1)

The line perpendicular to (1) is y = mx where m = (3/2). So the line is

y = (3/2)x …(2).

The coordinates of of M are got by solving for x and y from (1) and (2).

Thus y = (-2/3)x + 2 = (3/2)x or

(3/2)x + (2/3)x = 2, or

(9+4)x/6 = 2, or

x = 12/13 and y = (3/2)*(12/13) = 18/13.