How do you get the perpendicular to the equation 4x-3y equals 7?

Answer 1

Write the equation of the given line in standard form: y = mx + c

so: 3y = 4x - 7 or y = 4/3x - 7/3

The slope of the given line is 4/3.

The slope of the line perpendicular to it is the negative reciprocal (change the sign and flip the fraction over).

ie the perpendicular has slope -3/4

So the equation of the perpendicular is of the form y = -3/4x + d

or 4y = - 3x + 4d

or 3x + 4y = 4d.

To evaluate the value of the constant d (or 4d) you will need one point on the perpendicular line. Substitute the coordinates of that point for x and y in the above equation and you've got 4d.