Write an equation of the line passing through point p that is perpendicular to the given line. p(3,1), y=13x−5

The slope of a line perpendicular to another is (-1) multiplied by the

reciprocal of the slope of the other line.

Reasons:

The equation of the given line is; y = 13·x - 5

The point through which the perpendicular line passes = P(3, 1)

Solution:

The slope of a line, b, perpendicular to a line a with slope m is

The equation of the given line, y = 13·x - 5, is given in slope and intercept form, y = m·x + c

Therefore, the slope, m = 13

The slope of the perpendicular line in therefore,

Which gives the equation of the perpendicular line in point and slope form as follows;

13·y - 13 = 3 - x

13·y = 3 - x + 13 = 16 - x

The equation of the line is 13·y = 16 - x

Learn more about the equation of a line perpendicular to another line here:

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