What is the equation of a line perpendicular to 3x - y = 18 and passing through (2, 4)

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The equation of the line that is given, 3x - y = 18, can be written as y = 3x - 18. This is the slope, intercept form. The slope of the given line is 3. As the product of slope of two perpendicular lines is -1, the slope of the line to be determined is -1/3.

This line has to pass through the point (2, 4), the equation of the line is (y - 4)/(x - 2) = -1/3

=> 3(y - 4) = -(x - 2)

=> 3y - 12 = 2 -x

=> x + 3y - 14 = 0

The equation of the required line is x + 3y - 14 = 0

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