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

1 Answer
Jan 3, 2017

Answer:

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.