The equation of this graph is y = 2/3x - 4. What transformation would need to happpen for the equation of the line to be y = 2/3x? A. Shift the graph down 3 and left 2 B. Shift the graph right 3, down 2 C shift left 4 D. Shift the graph up 4
To transform the equation from y = 2/3x - 4 to y = 2/3x, the graph needs to shift up 4 units. Therefore, the correct answer is D. Shift the graph up 4.
To transform the equation y = 2/3x - 4 to y = 2/3x, the following transformation needs to happen:
A. Shift the graph down 3 and left 2.
Explanation:
The equation y = 2/3x - 4 represents a line with a slope of 2/3 and a y-intercept of -4. By shifting the graph down 3 units, we would be changing the y-intercept to -1 (original y-intercept - 3 = -4 - 3 = -7). By shifting the graph left 2 units, we would be changing the x-intercept to 2 (original x-intercept + 2 = 0 + 2 = 2).
Therefore, the correct answer is A. Shift the graph down 3 and left 2.
To find the transformation needed for the equation of the line to be y = (2/3)x, we need to compare it to the given equation y = (2/3)x - 4.
The given equation y = (2/3)x - 4 has a constant term of -4, which shifts the graph downward by 4 units. Therefore, to eliminate the constant term and make the equation y = (2/3)x, we need to shift the graph upward by 4 units.
Among the provided choices, shifting the graph upward is not an option. So, none of the given options match the required transformation of eliminating the constant term.