OG详解-OG5 数学2 Q8

Choice D is correct. A line in the xy-plane with a slope of m and a y-intercept of (0, b) can be defined by an equation in the form y = mx+b. It’s given that line r has a slope of 4 and passes through the point (0, 6). It follows that m = 4 and b = 6. Substituting 4 for m and 6 for b in the equation y = mx+b yields y = 4x+6. Therefore, the equation y = 4x+6 defines line r.
Choice A is incorrect. This equation defines a line that has a slope of -6, not 4, and passes through the point (0, 4), not (0, 6). Choice B is incorrect. This equation defines a line that has a slope of 6, not 4, and passes through the point (0, 4), not (0, 6). Choice C is incorrect. This equation defines a line that passes through the point (0, -6), not (0, 6).