For line h, the table shows three values of x and their corresponding values of y. Line k is the result of translating line h down 5 units in the xy-plane. What is the x-intercept of line k?

Question

Accepted Answer

Choice D is correct. For line h, the table shows three values of x and their corresponding values of y. We can determine the slope of line h using two points from the table, for example (18, 130) and (23, 160): m = 160 − 130 ⁄ 23 − 18 = 30 ⁄ 5 = 6. Substituting 6 for m in y = mx + b yields y = 6x + b. Substituting 130 for y and 18 for x yields 130 = 6(18) + b, or 130 = 108 + b, which gives b = 22. Thus, the equation of line h is y = 6x + 22. Since line k is the result of translating line h down 5 units, its equation is y = 6x + 22 − 5, or y = 6x + 17. The x-intercept of line k is the point where y = 0. Substituting 0 for y yields 0 = 6x + 17, which gives x = − 17 ⁄ 6 . Therefore, the x-intercept of line k is (− 17 ⁄ 6 , 0). Choice A is incorrect and may result from conceptual or calculation errors. Choice B is incorrect and may result from conceptual or calculation errors. Choice C is incorrect and may result from conceptual or calculation errors.

Want a deeper, personalized explanation?

Related questions