Final answer:
For the graph of dy + 3x = 2 to be parallel to the graph of x - 3y = 0, the value of d must be -9.
Step-by-step explanation:
To determine the value of d for which the graph of dy + 3x = 2 is parallel to the graph of x - 3y = 0 or the y-axis, we first need to understand the concept of the slope of a line.
The slope is a measure of how steep a line is, and it is calculated as the rise over the run (change in y over change in x). For two lines to be parallel, their slopes must be equal.
First, we convert the equation x - 3y = 0 into slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. This yields y = (1/3)x, meaning the slope of this line is 1/3. For the graph of dy + 3x = 2 to be parallel to this line, it must also have a slope of 1/3.
By rearranging dy + 3x = 2 into slope-intercept form, we get y = (-3/d)x + (2/d).
Therefore, to have a slope of 1/3, d must be -9 (-3/-9 = 1/3).