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 t 90 miles
3 hrs 135 miles
5 hrs 225 miles
6 hrs 270 miles
i need to show how to do it in steps.d
Use a proportion as I showed you in response to your last question.
To find the constant of proportionality and unit rate for the data in the table, you need to determine how the distance changes in relation to time. Let's go step-by-step:
Step 1: Choose two points from the table.
For this example, let's choose the points (2 hrs, 90 miles) and (5 hrs, 225 miles).
Step 2: Calculate the change in distance (Δd) and change in time (Δt) between the two points.
Δd = 225 miles - 90 miles = 135 miles
Δt = 5 hrs - 2 hrs = 3 hrs
Step 3: Calculate the constant of proportionality (k) by dividing the change in distance by the change in time.
k = Δd / Δt = 135 miles / 3 hrs = 45 miles/hr
Step 4: The constant of proportionality represents the unit rate, so the unit rate in this case is 45 miles per hour.
Step 5: Write the equation to represent the relationship between time (t) and distance (d).
The equation is: d = k * t
Substituting the known values, we have: d = 45t
Therefore, the equation to represent the relationship between time (t) and distance (d) is d = 45t, where d is the distance in miles and t is the time in hours.