Question

Given the table of values below, identify the constant of proportionality and write an equation to represent the relationship. You must show ALL work to earn full credit.

hour:2,4,6,8
miles: 120,240,360,480

Answer 1

To determine the constant of proportionality and write an equation representing the relationship between the hours and miles traveled, follow these steps:

1. **Set up the relationship**:
We want to express miles (m) as a function of hours (h). The relationship appears to be linear, which can be expressed as:
\[
m = k \cdot h
\]
where \(k\) is the constant of proportionality.

2. **Identify values**:
We will use the provided data points to find \(k\):
- When \(h = 2\), \(m = 120\)
- When \(h = 4\), \(m = 240\)
- When \(h = 6\), \(m = 360\)
- When \(h = 8\), \(m = 480\)

3. **Calculate the constant of proportionality \(k\)** using a few of the data points:
- For \(h = 2\):
\[
k = \frac{m}{h} = \frac{120}{2} = 60
\]
- For \(h = 4\):
\[
k = \frac{m}{h} = \frac{240}{4} = 60
\]
- For \(h = 6\):
\[
k = \frac{m}{h} = \frac{360}{6} = 60
\]
- For \(h = 8\):
\[
k = \frac{m}{h} = \frac{480}{8} = 60
\]

In all cases, we find that \(k = 60\).

4. **Write the equation**:
Now that we know \(k\), we can write the equation depicting the relationship:
\[
m = 60 \cdot h
\]

5. **Conclusion**:
The constant of proportionality is **60**, and the equation that represents the relationship between hours and miles is:
\[
m = 60h
\]

This means that for every hour traveled, 60 miles are covered.