Line p is defined by 2 y + 18 x = 9 . Line r is perpendicular to line p

Question

Line p is defined by 2 y + 18 x = 9 . Line r is perpendicular to line p in the xy -plane. What is the slope of line r ?

Accepted Answer

Choice C is correct. It&rsquo;s given that line r is perpendicular to line p in the xy -plane. This means that the slope of line r is the negative reciprocal of the slope of line p . If the equation for line p is rewritten in slope-intercept form y = m x + b , where m and b are constants, then m is the slope of the line and 0 , b is its y -intercept. Subtracting 18 x from both sides of the equation 2 y + 18 x = 9 yields 2 y = - 18 x + 9 . Dividing both sides of this equation by 2 yields y = - 9 x + 9 2 . It follows that the slope of line p is - 9 . The negative reciprocal of a number is - 1 divided by the number. Therefore, the negative reciprocal of - 9 is - 1 - 9 , or 1 9 . Thus, the slope of line r is 1 9 . Choice A is incorrect. This is the slope of line p , not line r . Choice B is incorrect. This is the reciprocal, not the negative reciprocal, of the slope of line p . Choice D is incorrect. This is the negative, not the negative reciprocal, of the slope of line p .

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