Question

1. this table represents a proportional relationship. number of people: 3, 5, 6, 9; number of chicken nuggets: 9, 15, 18, 27. what is the constant of proportionality? write an equation. based on the equation, if there are 18 children, how many chicken nuggets do you need?

Explanation:

Step1: Calculate the constant of proportionality

The constant of proportionality $k$ in a proportional relationship $y = kx$ (where $y$ is the number of chicken - nuggets and $x$ is the number of people) can be found by taking the ratio of $y$ to $x$. For example, when $x = 3$ and $y=9$, $k=\frac{y}{x}=\frac{9}{3}=3$. We can check with other pairs: for $x = 5,y = 15$, $\frac{15}{5}=3$; for $x = 6,y = 18$, $\frac{18}{6}=3$; for $x = 9,y = 27$, $\frac{27}{9}=3$. So the constant of proportionality $k = 3$.

Step2: Write the equation

The equation for a proportional relationship is $y=kx$. Since $k = 3$, the equation is $y = 3x$, where $y$ is the number of chicken - nuggets and $x$ is the number of people.

Step3: Find the number of chicken - nuggets for 18 people

Substitute $x = 18$ into the equation $y=3x$. Then $y=3\times18=54$.

Answer:

The constant of proportionality is 3.
The equation is $y = 3x$.
If there are 18 children, you need 54 chicken - nuggets.