If the graph of 27 x + 33 y = 297 is shifted down 5 units in the xy -plane,

Question

If the graph of 27 x + 33 y = 297 is shifted down 5 units in the xy -plane, what is the y -intercept of the resulting graph?

Accepted Answer

Choice A is correct. When the graph of an equation in the form A x + B y = C , where A , B , and C are constants, is shifted down k units in the xy -plane, the resulting graph can be represented by the equation A x + B y + k = C . It's given that the graph of 27 x + 33 y = 297 is shifted down 5 units in the xy -plane. Therefore, the resulting graph can be represented by the equation 27 x + 33 y + 5 = 297 , or 27 x + 33 y + 165 = 297 . Subtracting 165 from both sides of this equation yields 27 x + 33 y = 132 . 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 0 , y . Substituting 0 for x in the equation 27 x + 33 y = 132 yields 27 0 + 33 y = 132 , or 33 y = 132 . Dividing both sides of this equation by 33 yields y = 4 . Therefore, if the graph of 27 x + 33 y = 297 is shifted down 5 units, the y -intercept of the resulting graph is 0 , 4 . 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 27 x + 33 y = 297 shifted up, not down, 5 units. Choice D is incorrect and may result from conceptual or calculation errors.

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