Question

Write an equation of the line that passes through the point (6,2) and is perpendicular to the line y=3x+3

Answer 1

y = -
`(1)/(3)`x + 4

Explanation:

To find the slope of a perpendicular line, find the negative reciprocal of the slope.

The slope is 3 so the slope of the perpendicular line would be -
`(1)/(3)`

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Then use point slope form to find the equation of the perpendicular line:

y -
`y_(1)` = m (x -
`x_(1)` )

point = (6, 2)

slope = -
`(1)/(3)`

y - 2 = -
`(1)/(3)` (x - 6)

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If you want it in slope intercept form, you can just rearrange the equation:

y = 2 -
`(1)/(3)`x +2

y = -
`(1)/(3)`x + 4