What is the equation of the line that passes through the point (1,3) and is perpendicular to the line 2x+3y=15?
1 answer:
Answer:
3x -2y = -3
Step-by-step 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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<h3>form of the equation</h3>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'
<h3>constant</h3>The constant is chosen so the given (x, y) values satisfy the equation.
3(1) -2(3) = c' = -3
<h3>equation</h3>Then the equation of the perpendicular line through point (1, 3) is ...
3x -2y = -3
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<em>Additional comment</em>
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.
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