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What is the equation of the line that passes through (0,5) the point and is parallel to the graph of y = 7x+4 in the xy-plane? y = 5x
Correct answer: B (parsed from the explanation — this source omits an answer key for this item)
Explanation
Choice B is correct. The equation of a line in the xy-plane can be written in = + 0, slope-intercept form y mx b, where m is the slope of the line and ^ bh is its 0,5 = y-intercept. It’s given that the line passes through the point ^ h. Therefore, b 5. =7 +4 It’s also given that the line is parallel to the graph of y x , which means the =7 +4 line has the same slope as the graph of y x . The slope of the graph of =7 +4 = y x is 7. Therefore, m 7. Substituting 7 for m and 5 for b in the equation = + =7 +5 y mx b yields y x . 0,0 Choice A is incorrect. The graph of this equation passes through the point ^ h, 0,5 not ^ h, and has a slope of 5, not 7. Choice C is incorrect. The graph of this 0,0 0,5 equation passes through the point ^ h, not ^ h. Choice D is incorrect. The 0,7 0,5 graph of this equation passes through the point ^ h, not ^ h, and has a slope of 5, not 7.
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