OG详解-OG6 数学2 Q18

Choice B is correct. It’s given that line k is defined by y = 7x+1​8​. For an equation in slope-intercept form y = mx+b, m represents the slope of the line defined by this equation in the xy-plane and b represents the y-coordinate of the y-intercept of this line. Therefore, the slope of line k is 7. It’s also given that line j is perpendicular to line k in the xy-plane. Therefore, the slope of line j is the opposite reciprocal of the slope of line k. The opposite reciprocal of 7 is - 17​​. Therefore, the slope of line j is -17​​ .
Choice A is incorrect. This is the opposite reciprocal of the y-coordinate of the y-intercept, not the slope, of line k. Choice C is incorrect. This is the y-coordinate of the y-intercept of line k, not the slope of line j. Choice D is incorrect. This is the slope of a line that is parallel, not perpendicular, to line k.