Question

⑤determine the constant of proportionality for the relationship and complete the table. what does the constant of proportionality tell you about the situation? show all work!
white paint (cups) | red paint (cups)
2 | 4
1 |
7 |
| 80

Explanation:

Step1: Find the constant of proportionality

The constant of proportionality $k$ in a proportional relationship $y = kx$ (let $y$ be red - paint and $x$ be white - paint) is found by $k=\frac{y}{x}$. Given $x = 2$ and $y = 4$, then $k=\frac{4}{2}=2$.

Step2: Complete the table for $x = 1$

When $x = 1$, using $y=kx$ with $k = 2$, we have $y=2\times1 = 2$.

Step3: Complete the table for $x = 7$

When $x = 7$, using $y = kx$ with $k = 2$, we have $y=2\times7=14$.

Step4: Complete the table for $y = 80$

When $y = 80$, since $y = kx$ and $k = 2$, then $x=\frac{y}{k}=\frac{80}{2}=40$.

Step5: Interpret the constant of proportionality

The constant of proportionality $k = 2$ means that for every cup of white paint, 2 cups of red paint are used.

Answer:

White paint (cups)	Red paint (cups)
1	2
7	14
40	80

The constant of proportionality is 2, which means for every cup of white paint, 2 cups of red paint are used.