Question

1. this table represents a proportional relationship. complete the table. number of dogs pounds of dog food 25 5 20 3 1 constant of proportionality: __________ equation y = ______ based on the equation, if you have 20 pounds of dog food, how many dogs can you feed?

Explanation:

Step1: Find the constant of proportionality

Let $x$ be the number of dogs and $y$ be the pounds of dog - food. The constant of proportionality $k$ is given by $k=\frac{y}{x}$. Using the first row where $x = 25$ and $y = 5$, we have $k=\frac{5}{25}=\frac{1}{5}=0.2$.

Step2: Find the value of $y$ when $x = 20$

We know that $y=kx$. Substituting $x = 20$ and $k = 0.2$, we get $y=0.2\times20 = 4$.

Step3: Find the value of $x$ when $y = 3$

Since $y = kx$, then $x=\frac{y}{k}$. Substituting $y = 3$ and $k = 0.2$, we have $x=\frac{3}{0.2}=15$.

Step4: Find the value of $y$ when $x = 1$

Using $y=kx$ with $x = 1$ and $k = 0.2$, we get $y=0.2\times1 = 0.2$.

Step5: Write the equation

The equation for the proportional relationship is $y = 0.2x$.

Step6: Find the number of dogs for 20 pounds of food

If $y = 20$, then from $y=0.2x$, we can solve for $x$. Rearranging the equation gives $x=\frac{y}{0.2}$. Substituting $y = 20$, we get $x=\frac{20}{0.2}=100$.

Answer:

Number of dogs	Pounds of dog food
20	4
15	3
1	0.2

Constant of Proportionality: $0.2$
Equation: $y = 0.2x$
If you have 20 pounds of dog food, you can feed 100 dogs.