Math / Data & Statistics

Question $\begin{array}{|c|c|} \hline x \text{- Number of Days} & y \text{- Cost} \\ \hline 6 & 2 \\ \hline 9 & 3 \\ \hline 24 & 8 \\ \hline 3 & 1 \\ \hline \end{array}$
Determine the constant of proportionality between the number of days ( $x$ ) and the cost ( $y$ ) based on the given data.

Studdy Solution

STEP 1

1. The relationship between the number of days $x$ and the cost $y$ is directly proportional.
2. The constant of proportionality $k$ can be expressed as $y = kx$ .

STEP 2

1. Verify the assumption of direct proportionality.
2. Calculate the constant of proportionality $k$ for each pair.
3. Confirm consistency of $k$ across all data pairs.

STEP 3

Verify the assumption of direct proportionality by checking if the ratio $\frac{y}{x}$ is constant for each data pair.

STEP 4

Calculate $\frac{y}{x}$ for each pair:
- For $(6, 2)$ : $\frac{2}{6} = \frac{1}{3}$ - For $(9, 3)$ : $\frac{3}{9} = \frac{1}{3}$ - For $(24, 8)$ : $\frac{8}{24} = \frac{1}{3}$ - For $(3, 1)$ : $\frac{1}{3} = \frac{1}{3}$

STEP 5

Since the ratio $\frac{y}{x}$ is constant and equal to $\frac{1}{3}$ for all pairs, the constant of proportionality $k$ is $\frac{1}{3}$ .
The constant of proportionality is:
$\boxed{\frac{1}{3}}$

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms