Question
time (hours) 2 3 5 6
distance (miles) 90 135 225 270
The constant of proportionality is
and the equation for this relationship is
.
distance (miles) 90 135 225 270
The constant of proportionality is
and the equation for this relationship is
.
Answers
GPT-4o mini
To find the constant of proportionality and the equation for the relationship between time and distance, we can start by determining how distance relates to time.
The relationship between distance and time can be described by the formula:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
1. **Calculate the speed for each data point:**
- For \(2\) hours: \(\frac{90}{2} = 45\) miles per hour
- For \(3\) hours: \(\frac{135}{3} = 45\) miles per hour
- For \(5\) hours: \(\frac{225}{5} = 45\) miles per hour
- For \(6\) hours: \(\frac{270}{6} = 45\) miles per hour
The constant speed (or constant of proportionality) is \(45\) miles per hour.
2. **Write the equation for this relationship:**
Using the constant speed, the equation relating distance (d) and time (t) can be expressed as:
\[ d = 45t \]
In summary:
- **The constant of proportionality is** \(45\) (miles per hour).
- **The equation for this relationship is** \(d = 45t\).
The relationship between distance and time can be described by the formula:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
1. **Calculate the speed for each data point:**
- For \(2\) hours: \(\frac{90}{2} = 45\) miles per hour
- For \(3\) hours: \(\frac{135}{3} = 45\) miles per hour
- For \(5\) hours: \(\frac{225}{5} = 45\) miles per hour
- For \(6\) hours: \(\frac{270}{6} = 45\) miles per hour
The constant speed (or constant of proportionality) is \(45\) miles per hour.
2. **Write the equation for this relationship:**
Using the constant speed, the equation relating distance (d) and time (t) can be expressed as:
\[ d = 45t \]
In summary:
- **The constant of proportionality is** \(45\) (miles per hour).
- **The equation for this relationship is** \(d = 45t\).