OG详解-OG1 数学2 Q26

Choice B is correct. Two lines are perpendicular if their slopes are negative reciprocals,meaning that the slope of the first line is equal to  -1 divided by the slope of the second line. Each equation in the given pair of equations can be written in slope-intercept form, y = mx + b, where m  is the slope of the graph of the equation in the xy-plane and  (0,b) is they-intercept. For the first equation,  5x +7y = 1, subtracting 5x from both sides gives 7y =-5x +1, and dividing both sides of this equation by 7 gives y = -5​7​x +1​7​. Therefore, the slope of the graph of this equation is -5​7​. For the second equation,  ax + by = 1, subtracting ax from both sides gives by =-ax +1, and dividing both sides of this equation by b gives y = -ab​​x + 1​b​. Therefore, the slope of the graph of this equation is -a​b​. Since the graph of the given pair of equations is a pair of perpendicular lines, the slope of the graph of the second equation,  -a​b​, must be the negative reciprocal of the slope of the graph of the first equation,  -5​7​. The negative reciprocal of  -5​7​is −1(−57​)​​ or 7​5​ . Therefore，. Similarly，rewriting the equations in choice B in slope-intercept form yields . It follows that the slope of the graph of the first equation in choice B is  -a2b​​ . Since  ab​​ = - 7​5​ ，-a2b is equal to .  Since 710​​  is the negative reciprocal of -107​​ , the pair of equations in choice B represents a pair of perpendicular lines.
Choice A is incorrect and may result from conceptual or calculation errors.
Choice C is incorrect and may result from conceptual or calculation errors.
Choice D is incorrect and may result from conceptual or calculation errors.