Line r in the xy-plane has a slope of 4 and passes through the point (0, 6). Which equation defines line r ?

Question

Accepted Answer

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).

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