Line k is defined by y = 7 x + 1 8 . Line j is perpendicular to line k

Question

Line k is defined by y = 7 x + 1 8 . Line j is perpendicular to line k in the xy -plane. What is the slope of line j ?

Accepted Answer

Choice B is correct. It's given that line k is defined by y = 7 x + 1 8 . For an equation in slope-intercept form y = m x + 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&rsquo;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 - 1 7 . Therefore, the slope of line j is - 1 7 . 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 .

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