find the constant of proportionality and unit rate for the data in the table. Then write the equation to represent the relationship between time t and distance d
Time Distance
2 hrs 90 miles
3 hrs 135 miles
5 hrs 225 miles
6 hrs 270 miles
i need to show how to do it in steps.
1 hr 45 miles
Whats the unit rate? And how would i show my work?
2/90 = 1/x
Cross multiply and solve for x.
To find the constant of proportionality and unit rate for the data in the table and write the equation to represent the relationship between time and distance, follow these steps:
1. Identify two pairs of values from the table. Let's choose (2 hrs, 90 miles) and (3 hrs, 135 miles).
2. Determine the change in distance and change in time between the two pairs. For (2 hrs, 90 miles) to (3 hrs, 135 miles), the change in distance is 135 - 90 = 45 miles, and the change in time is 3 - 2 = 1 hour.
3. Calculate the constant of proportionality by dividing the change in distance by the change in time: constant of proportionality = change in distance / change in time. In this case, it is 45/1 = 45.
4. The unit rate can be found by dividing the constant of proportionality by 1 unit of time. In this case, the unit rate is 45 miles / 1 hour = 45 miles per hour.
5. To write the equation that represents the relationship between time (t) and distance (d), use the constant of proportionality (k) and the variable representing time (t): d = k * t. Substituting the value of the constant of proportionality we found in step 3 (k = 45), the equation becomes d = 45t.
Therefore, the constant of proportionality is 45 and the unit rate is 45 miles per hour. The equation that represents the relationship between time (t) and distance (d) is d = 45t.