Find the line which is perpendicular to 3y+6x-7=0 and passes through the point A(4, -7)

Answer 1

GENERAL THEORY

A line perpendicular to another one of the form y = mx + C will have a slope as negative inverse of slope m.

So, perpendicular line will have the form

y = (-1/m)*x + B

SOLUTION:

First convert the given equation in to the usual linear form

y = -2x + 7/3

Slope of this line is therefore, m = -2

The slope of the perpendicular line will be 1/2, and the equation will have the form

y = (1/2)*x + B

where B is still to be determined.

Since A (4, -7) lies on this perpendicular line, you can substitute these in the equation

-7 = (1/2)*4 + B

Solve for B

B = -9

Therefore, the complete equation for the perpendicular can be written as

y = (1/2)*x - 9

Alternatively, multiplying out the two sides of the equation by 2,

2y = x - 19