Math CentralQuandaries & Queries


Question from Daphne, a student:

Does anyone know how to find a line perpendicular to -3x=4y=20 and passes through the point (-12,0)?

We have two responses for you

Hi Daphne,

Write the line in slope intercept form, y = mx + b. The value of m is then the slope of the line.

If a line has slope m then any line perpendicular to this line has slope - 1/m, the negative reciprocal of m. Take the value of m you found in the previous paragraph, find its negative reciprocal and then write the equation of the line with that slope and through the point (-12, 0).

If you need further assistance write back,


Hi Daphne.

Here's a similar problem to yours and how I solve it:

Question. What is the equation of the line perpendicular to - 9x + 2y = 20 which passes through (8,-1)?

Answer. The slopes of perpendicular lines have slopes that are the negative reciprocal of each other. When a line equation is in Ax + By = C form (as the one above is), then the slope is m = -A/B. So the perpendicular slope is B/A. Therefore, we can just swap the constants and change one of the signs!

This means the equation of any line perpendicular to this one is 2x + 9y = ?. "A" was replaced with "-B" and "B" was replaced with "A".

Now I simply plug in the (x,y) value I was given to finish it off: 2(8) + 9(-1) = 7.

So the answer is 2x + 9y = 7.

Now you try your problem.

Stephen La Rocque.

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