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Algebra / Linear equations in two variables Difficulty: Medium

Line k is defined by y=-173x+5. Line j is perpendicular to line k in the xy-plane. What is the slope of line j ?

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Explanation

The correct answer is 3 17 . It’s given that line j is perpendicular to line k in the xy-plane. This means that the slope of line j is the negative reciprocal of the slope of line k . The equation of line k , y=-173x+5, is written in slope-intercept form y = m x + b , where m is the slope of the line and b is the y-coordinate of the y-intercept of the line. It follows that the slope of line k is - 17 3 . The negative reciprocal of a number is -1 divided by the number. Therefore, the negative reciprocal of - 17 3 is -1-173, or 3 17 . Thus, the slope of line j is 3 17 . Note that 3/17, .1764, .1765, and 0.176 are examples of ways to enter a correct answer.