OG详解-OG2 数学2 Q16

Choice C is correct. It’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 = mx + b, where m  and b are constants, then m  is the slope of the line and (0, b) is its y-intercept. Subtracting 18x from both sides of the equation 2y +18x = 9 yields 2y = -18x +9 . Dividing both sides of this equation by 2 yields y =-9x +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.