To identify the constant of proportionality in a graph representing the relationship between the number of sodas and the price, you would typically look for a straight line that passes through the origin (0,0). The constant of proportionality can be determined by calculating the ratio of the price to the number of sodas at any point on that line.
For example, if the graph shows that 1 soda costs $1.50, 2 sodas cost $3.00, and 3 sodas cost $4.50, you can derive the constant of proportionality (k) using the formula:
\[ k = \frac{\text{Price}}{\text{Number of sodas}} \]
So, for the above example, the constant of proportionality would be:
\[ k = \frac{1.50}{1} = 1.50, \quad \frac{3.00}{2} = 1.50, \quad \frac{4.50}{3} = 1.50 \]
This indicates a constant ratio, meaning every soda costs $1.50.
True Statement:
"The price of sodas is directly proportional to the number of sodas purchased, with each soda costing the constant amount of the identified proportionality (in this case, $1.50)."
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