Question

determine the constant of proportionality for the relationship and complete the table. what does the constant of proportionality tell you about the situation? 2. the constant of proportionality is 1.5. the paint is made with cups of blue paint for every __ cup of red paint. 4. the constant of proportionality is __. red paint (cups) blue paint (cups) 2 3 1 1.5 6 9 40 60 red paint (cups) yellow paint (cups) 2 8 1 4 12.5 50

Explanation:

Step1: Recall the formula for constant of proportionality

For a proportional relationship $y = kx$, $k=\frac{y}{x}$.

Step2: Calculate constant for red - blue paint

For the red - blue paint relationship, using the first row of the table where $x = 2$ (red paint) and $y = 3$ (blue paint), $k=\frac{y}{x}=\frac{3}{2}=1.5$. It means there are 1.5 cups of blue paint for every 1 cup of red paint.

Step3: Calculate constant for red - yellow paint

Using the first row of the red - yellow paint table where $x = 2$ (red paint) and $y = 8$ (yellow paint), $k=\frac{y}{x}=\frac{8}{2}=4$.

Answer:

The constant of proportionality for the red - blue paint relationship is 1.5. It means there are 1.5 cups of blue paint for every cup of red paint. The constant of proportionality for the red - yellow paint relationship is 4.