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.
3 answers
A is 45
what else
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.
- 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.