OG详解-OG3 数学1 Q11

Choice B is correct. The equation of a line in the xy-plane can be written in slope-intercept form y = mx + b, where m  is the slope of the line and (0, b) is its y-intercept. It’s given that the line passes through the point  (0, 5). Therefore, b = 5. It’s also given that the line is parallel to the graph of  y = 7x + 4, which means the line has the same slope as the graph of  y = 7x + 4. The slope of the graph of y = 7x + 4 is 7. Therefore, m = 7. Substituting 7 for m and 5  for b in the equation y = mx + b yields y = 7x +5.
Choice A is incorrect. The graph of this equation passes through the point  (0, 0), not (0, 5), and has a slope of  5, not  7. Choice C is incorrect. The graph of this  equation passes through the point  (0, 0), not  (0, 5). Choice D is incorrect. The graph of this equation passes through the point  (0, 7), not  (0, 5), and has a slope of 5, not 7.