Question

1. this table represents a proportional relationship. complete the table. number of hours number of miles 8 16 8 5 1 constant of proportionality: ____________ equation y = ______ based on the equation, how long will it take for the snail to travel 36 miles? 4) this table represents a proportional relationship. complete the table.

Explanation:

Step1: Find the constant of proportionality

The constant of proportionality $k$ in a proportional relationship $y = kx$ (where $y$ is the number of miles and $x$ is the number of hours) can be found using the given pair $(x = 8,y = 16)$. So, $k=\frac{y}{x}=\frac{16}{8}=2$.

Step2: Find the missing number of hours when $y = 8$

Using the formula $y = kx$, and $k = 2,y = 8$, we can solve for $x$. Rearranging gives $x=\frac{y}{k}=\frac{8}{2}=4$.

Step3: Find the missing number of miles when $x = 5$

Using $y=kx$ with $k = 2,x = 5$, we get $y=2\times5 = 10$.

Step4: Find the missing number of miles when $x = 1$

Using $y=kx$ with $k = 2,x = 1$, we get $y=2\times1=2$.

Step5: Find the time to travel 36 miles

Using $y = kx$ and $y = 36,k = 2$, we solve for $x$. Rearranging gives $x=\frac{y}{k}=\frac{36}{2}=18$.

Answer:

Number of hours	Number of miles
4	8
5	10
1	2

Constant of Proportionality: 2
Equation $y = 2x$
It will take 18 hours for the snail to travel 36 miles.