Final answer:
The constant of proportionality between the points (3, 4.5) and (6, 9) is 1.5. This value is obtained by dividing the y-coordinates by the x-coordinates for each point, and it corresponds to option c. 3/2.
Step-by-step explanation:
To find the constant of proportionality between the points (3, 4.5) and (6, 9), you can write it as the ratio of the y-coordinates (output) to the x-coordinates (input). The formula for the constant of proportionality 'k' is y = kx, where 'y' is the output, 'x' is the input, and 'k' is the constant of proportionality.
Let's calculate for each point:
- For (3, 4.5): 4.5 = k * 3
- For (6, 9): 9 = k * 6
Solving for 'k' in each case gives us:
- 4.5 / 3 = k, which simplifies to 1.5 = k
- 9 / 6 = k, which again simplifies to 1.5 = k
Therefore, the constant of proportionality for both points is the same, 1.5, which corresponds to option c. 3/2.