Final answer:
The constant of proportionality for the given values of x and y (where x=1, 2, 3 and y=3, 6, 9) is 3. This constant is found by dividing each y-value by the corresponding x-value. It is also represented by the slope of the line in the equation y=9+3x.
Step-by-step explanation:
The question asks us to determine the constant of proportionality based on the given values of x (1, 2, 3) and y (3, 6, 9). The constant of proportionality is the ratio between two quantities that are directly proportional to each other. In this case, the values provided create a set of ordered pairs: (1, 3), (2, 6), and (3, 9). To find the constant, we divide each y-value by its corresponding x-value.
For the first pair (1, 3):
3 ÷ 1 = 3
For the second pair (2, 6):
6 ÷ 2 = 3
And for the third pair (3, 9):
9 ÷ 3 = 3
In each case, the ratio (y divided by x) is 3, indicating that the constant of proportionality is 3. This means that y is directly proportional to x and increases by 3 units for every 1 unit increase in x. This is also reflected in the given equation y = 9 + 3x, where the coefficient of x (3) represents the slope of the line and serves as the constant of proportionality when the y-intercept is not involved (the term 9 represents the y-intercept).