Use the table to answer the following questions.
Time (hours) Distance (miles)
2 90
3 135
5 225
6 270
Find the constant of proportionality.
Use the constant of proportionality to write a unit rate for the data in the table.
Write an equation to represent the relationship between time, t, and distance, d.
To find the constant of proportionality, you can divide the distance by the time at any point. For example:
- At 3 hours, the distance is 135 miles. So the constant of proportionality is 135 รท 3 = 45.
To write a unit rate, we use the constant of proportionality as the coefficient of the variable in the equation. In this case, the unit rate represents the speed in miles per hour (mph), or the distance traveled in one hour. Therefore:
- The unit rate is 45 miles per hour (mph).
To write an equation to represent the relationship between time, t, and distance, d, we can use the formula for direct variation, which is:
d = kt
where k is the constant of proportionality. Substituting the value of k that we found earlier, we get:
d = 45t
This equation means that the distance traveled (d) is directly proportional to the time taken (t), with a constant rate of 45 miles per hour.
what else
To find the constant of proportionality, we need to compare the change in distance to the corresponding change in time. Let's take the first two data points: (2, 90) and (3, 135).
The change in distance is 135 - 90 = 45 miles, and the change in time is 3 - 2 = 1 hour.
To find the constant of proportionality, we divide the change in distance by the change in time:
45 miles / 1 hour = 45 miles/hour.
Therefore, the constant of proportionality is 45 miles/hour.
To write a unit rate for the data in the table, we will use the constant of proportionality. Since the constant of proportionality represents the rate at which distance changes with respect to time, our unit rate will be "45 miles/hour."
To write an equation that represents the relationship between time, t, and distance, d, we can use the constant of proportionality. The equation is:
d = k * t
Where d represents the distance, t represents the time, and k represents the constant of proportionality. In our case, the equation is:
d = 45t.