sat suite question viewer
If the graph of is shifted down units in the xy-plane, what is the y-intercept of the resulting graph?
Explanation
Choice A is correct. When the graph of an equation in the form , where , , and are constants, is shifted down units in the xy-plane, the resulting graph can be represented by the equation . It's given that the graph of is shifted down units in the xy-plane. Therefore, the resulting graph can be represented by the equation , or . Subtracting from both sides of this equation yields . The y-intercept of the graph of an equation in the xy-plane is the point where the line intersects the y-axis, represented by the point . Substituting for in the equation yields , or . Dividing both sides of this equation by yields . Therefore, if the graph of is shifted down units, the y-intercept of the resulting graph is .
Choice B is incorrect and may result from conceptual or calculation errors.
Choice C is incorrect. This is the y-intercept of the graph of shifted up, not down, units.
Choice D is incorrect and may result from conceptual or calculation errors.