https://file.aiquickdraw.com/mathbot/file/1725925029678kthl4ohm.jpg

The problem provided describes a situation where the number of miles driven is directly proportional to the number of gallons used. To write the proportional equation for \( m \) (the number of miles driven) in terms of \( g \) (the number of gallons used), we need to establish the proportionality constant based on the data given.

Here’s the process:

### Step 1: Determine the constant of proportionality.
The equation of direct proportionality is:
\[
m = k \cdot g
\]
where \( k \) is the constant of proportionality.

We can use the data from the table to find \( k \). Let's use the first data point: 
- \( g = 12 \) gallons results in \( m = 568.8 \) miles driven.

Thus, we can solve for \( k \) using the formula:
\[
k = \frac{m}{g} = \frac{568.8}{12} = 47.4
\]

### Step 2: Write the equation.
Now that we know \( k = 47.4 \), the proportional equation becomes:
\[
m = 47.4 \cdot g
\]

### Step 3: Verify with other data points.
To confirm the consistency, let’s check the other data points:

- For \( g = 47 \):
\[
m = 47.4 \cdot 47 = 2227.8 \quad \text{(which matches the table value exactly)}.
\]

- For \( g = 49 \):
\[
m = 47.4 \cdot 49 = 2322.6 \quad \text{(which matches the table value exactly)}.
\]

Thus, the proportional equation is verified.

### Final Answer:
The proportional equation is:
\[
m = 47.4 \cdot g
\]

Let me know if you'd like more details or have any questions! Here are some related questions to consider:

1. How would the equation change if the relationship were inverse proportionality instead of direct proportionality?
2. What is the significance of the constant \( k \) in real-life terms?
3. Can you predict the number of miles Adam would drive if he used 55 gallons?
4. What would happen to the miles driven if the number of gallons used doubled?
5. How can we visually represent this relationship on a graph?

**Tip**: When working with direct proportionality, always check that all data points fit the same proportional constant to confirm consistency.

The table below shows that the number of miles driven by Adam is directly proportional to the number of gallons he used. If m represents the number of miles driven for any number of gallons used, g, write a proportional equation for m in terms of g that matches the context.

Learn how to establish a proportional equation based on the number of miles driven and gallons used. This problem involves direct proportionality and provides a step-by-step solution. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation