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What is the equation of the line that passes through the point (1,3) and is perpendicular to the line 2x+3y=15?

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Answer:

3x -2y = -3

Explanation:

The perpendicular line will have a slope that is the negative reciprocal of the slope of the given line. The constant in its equation will ensure the line goes through the desired point.

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form of the equation

The equation for the given line is in standard form:

ax +by = c . . . . . where a>0 and a, b, c are mutually prime

The equation of the perpendicular line can be written ...

bx -ay = c' . . . . . where c' is a new constant

For a=2, b=3, the equation of the perpendicular will be ...

3x -2y = c'

constant

The constant is chosen so the given (x, y) values satisfy the equation.

3(1) -2(3) = c' = -3

equation

Then the equation of the perpendicular line through point (1, 3) is ...

3x -2y = -3
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Additional comment

For the standard-form equation shown, the slope of the line is ...

m = -a/b

The negative reciprocal slope is ...

-1/m = -1/(-a/b) = b/a

This is the original slope equation with a and b swapped, and one of them negated.

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The graph confirms the new equation.

What is the equation of the line that passes through the point (1,3) and is perpendicular-example-1
User Cory Harper
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