Question

Zoe says that the graph of the equation y = 3(x+4) is the same as the graph of y=3x, only translated upwards by 4 units. Is Zoe correct?

A. Yes, Zoe is correct.
B. No, Zoe is not correct.
C. Zoe is partially correct.
D. The information is insufficient to determine.

Answer 1

Zoe's statement that the graph of y = 3(x+4) is the same as y = 3x translated upwards by 4 units is incorrect. The correct transformation is a horizontal translation to the left by 4 units.

Step-by-step explanation:

Zoe is not correct. The equation y = 3(x+4) represents a line that is translated horizontally to the left by 4 units, not vertically. We can show this by expanding the equation to y = 3x + 12. This shows that the y-intercept is at 12, not the original 0 as it would be in the equation y = 3x. The slope, represented by 'm', remains 3 in both equations, indicating that the steepness of the line has not changed. However, the addition of 4 within the parentheses affects the x-values, leading to a horizontal translation.