When given the equation of a line that is perpendicular to the one you are interested in and a point on the line of interest, finding an equation for the line of interest is very straight forward.

Suppose you have a line given by the equation y=5x+2.

Find the equation of a line that passes through the point (2,3) and is perpendicular to the above line.

Because the line you are trying to describe is perpendicular to the one given, its slope must be the negative reciprocal of the slope of the given line.

In order to find the slope easily, put the equation of the given line in slope-intercept form if it already is not in that form.

Given line in slope-intercept form (y=mx+b)

Slope

Slope InputOutput

y-coordinate of a point on the line

x-coordinate of the same point on the line

Substitute in values and simplify

Equation of the line in point-slope form

Distribute

Write equation in slope-intercept form (y=mx+b)

Combine constant terms

Equation of the line of interest in slope-intercept form