Question

How do you find equation of line which is perpendicular to the line `2x-3y=5` and passes through the point (2,1)?

Answer 1

Swap the coefficients, make one negative, and then use the point to solve for the new constant.

Explanation:

When given the equation of a line in the form:

`ax + by = c`

It is very easy to make a line that is perpendicular to the given line:

1. Swap a and b
2. Change the sign of either a or b
3. Make the right side an arbitrary constant, k

The two possible results are shown below:

`bx - ay = k" [1]"`

or

`-bx + ay = k" [2]"`

For the given line, `2x - 3y = 5`, `a = 2 and b = -3`, therefore, we shall use form of equation [2], because it makes both constants positive:

`3x + 2y = k" [3]"`

Given the point `(2,1)`, we can find the value of k by substituting 2 for x and 1 for y into equation [3]:

`3(2) + 2(1) = k" [3]"`

`k = 7`

Substitute 7 for k into equation [3]:

`3x + 2y = 7" [4]"`

Equation [4] is the answer.