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12 = + Line k is defined by y 6x 4. Line j is parallel to line k in the xy-plane and passes through the point 0,5. Which equation defines line j? ^ h
Correct answer: A (parsed from the explanation — this source omits an answer key for this item)
Explanation
Choice A is correct. An equation that defines a line in the xy-plane can be written = + 0, as y mx b, where m is the slope of the line and ^ bh is its y-intercept. It’s =6 +4 given that line k is defined by the equation y x ; therefore, the slope of line k is 6. Since line j is parallel to line k in the xy-plane and parallel lines have equal slopes, it follows that the slope of line j is 6. It’s also given that line j 0,5 passes through the point ^ h, which is its y-intercept. Substituting 6 for m and = + =6 +5 5 for b in the equation y mx b yields y x . Therefore, the equation =6 +5 y x defines line j. - Choice B is incorrect. This equation defines a line that has a slope of 5, not 6. - Choice C is incorrect. This equation defines a line that has a slope of 6, not 6. Choice D is incorrect. This equation defines a line that has a slope of 5, not 6.
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