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A line in the xy-plane has a slope of 1/9 and passes (0,14) through the point. Which equation represents this line? y = − x−14
Correct answer: D (parsed from the explanation — this source omits an answer key for this item)
Explanation
Choice D is correct. The equation of a line in the xy-plane can be written as = + 0, y mx b, where m represents the slope of the line and ^1 bh represents the 1 = y-intercept of the line. It’s given that the slope of the line is 9. It follows that m 9. 0,14 =14 It’s also given that the line passes through the point ^ h. It follows that b . 1 14 = + = 1 +14 Substituting 9 for m and for b in y mx b yields y 9x . Thus, the = 1 +14 equation y 9x represents this line. 1 - Choice A is incorrect. This equation represents a line with a slope of 9 and a 0,-14 y-intercept of ^ h. Choice B is incorrect. This equation represents a line with - 1 0,14 a slope of 9 and a y-intercept of ^ h. Choice C is incorrect. This equation 1 0,-14 represents a line with a slope of 9 and a y-intercept of ^ h.
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