Question in-the
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 ?
In the xy -plane, line k is defined by . Line j is perpendicular to line
Hard-difficulty · SAT Math · Linear Functions — Parallel/perpendicular line relationships. Read the question above, select your answer, and check the full explanation below to understand exactly why the correct choice works.
Answer explanation
Choice D is correct. It’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’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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