Create your own question relating to a table of data and finding a constant of proportionality, unit rate, or equation representation.
Question:
The table below shows the distance traveled by a car over time. Use the data to find the constant of proportionality, unit rate, and equation representation.
| Time (hours) | Distance Traveled (miles) |
|--------------|--------------------------|
| 1 | 50 |
| 2 | 100 |
| 3 | 150 |
| 4 | 200 |
| 5 | 250 |
To find the constant of proportionality, unit rate, and equation representation, we need to analyze the data and identify any patterns or relationships.
Step 1: Calculate the unit rate
To find the unit rate, we divide the distance traveled by the time taken. Let's choose any two points from the table. For example, let's consider the first two points at time 1 hour and time 2 hours.
Unit rate = (Distance Traveled) / (Time Taken) = (100 miles - 50 miles) / (2 hours - 1 hour) = 50 miles/hour
So, the unit rate is 50 miles per hour.
Step 2: Find the constant of proportionality
The constant of proportionality represents the ratio between the two variables, distance, and time. To find it, we divide the distance traveled by the time taken for each point in the table. Let's choose any two points again, for example, the first and second points.
Constant of proportionality = (Distance Traveled) / (Time Taken) = (100 miles - 50 miles) / (2 hours - 1 hour) = 50 miles/hour
So, the constant of proportionality is 50 miles per hour.
Step 3: Equation representation
Using the constant of proportionality, we can write an equation to represent the relationship between distance and time. The equation is in the form y = kx, where y represents the distance traveled and x represents the time.
The equation representing the relationship between distance and time for this scenario is:
Distance Traveled = Constant of Proportionality * Time Taken
Distance Traveled = 50 miles/hour * Time Taken
Therefore, the equation representation is Distance Traveled = 50 * Time Taken.
By following these steps, we have found the constant of proportionality (50 miles per hour), unit rate (50 miles per hour), and equation representation (Distance Traveled = 50 * Time Taken) for the given table of data.