Question

How to write an equation for the line perpendiculer and trhough the given ppoint?

Answer 1

A method that always works is to find the slope of the given line, then find the negative reciprocal of that. Your result will be the slope of the perpendicular line. Using this slope and the given point, fill in the parameters of the point-slope form of the equation of a line.

For m = slope of given line and (h, k) = given point, the perpendicular line will be
  y = (-1/m)(x -h) +k

Often, this equation can be simplified to another appropriate form, such as slope-intercept form (y = mx+b) or standard form (ax+by=c).

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The slope of a given line can be found by solving its equation for y. The slope is the coefficient of x in that solution. If the given line is characterized by two points, (x1, y1) and (x2, y2), then its slope is m = (y2-y1)/(x2-x1).

In the unusual case where the given line is vertical (x=<some constant>), the slope of the perpendicular line is zero, and the line you want becomes y=k.