In the xy -plane, line k is defined by . Line j is perpendicular to line k , and the

Question

In the xy -plane, line k is defined by . Line j is perpendicular to line k , and the y -intercept of line j is . Which of the following is an equation of line j ?

Accepted Answer

Choice D is correct. It&rsquo;s given that line j is perpendicular to line k and that line k is defined by the equation . This equation can be rewritten in slope-intercept form, , where m represents the slope of the line and b represents the y -coordinate of the y -intercept of the line, by subtracting x from both sides of the equation, which yields . Thus, the slope of line k is . Since line j and line k are perpendicular, their slopes are opposite reciprocals of each other. Thus, the slope of line j is 1. It&rsquo;s given that the y -intercept of line j is . Therefore, the equation for line j in slope-intercept form is , which can be rewritten as . Choices A, B, and C are incorrect and may result from conceptual or calculation errors.

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