Find the line perpendicular to a line through a given point. Learn how to write the equation of a line that is perpendicular to a given line. The equation of a line is such that its highest exponent on its variable(s) is 1. (i.e. there are no exponents in its variable(s)). There are various forms which we can write the equation of a line: the point-slope form, the slope-intercept form, the standard form, etc.
When given a point (x, y) through which a line passes and the slope (m) of the line, the equation of the line is given by y - y1 = m(x - x1). For perpendicular lines, the product of their slopes is -1. Thus given the equation of a line and a point through which the line perpendicular to the given line passes, then the slope of the second line is equal to the negative of the reciprocal of the slope of the given line. Having found the slope, we can then use the formula stated above together with the given point to find the required equation.
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