Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Use the table to answer the following questions.
Time (hours) Distance (miles)
2 90
3 135
5 225
6 270
A: Find the constant of proportionality.
B: Use the constant of proportionality to write a unit rate for the data in the table.
C: Write an equation to represent the relationship between time, t, and distance, d.
A: 135-90=45 3-2=1
(135-90)÷(3-2) =45
B: unit rate=45t/d
C: d=45t
This is what I got for the answer.
divide output by input, since y=kx
ok thx
LuJent a Roblox player is right.
To find the constant of proportionality, we need to determine the ratio between the distance traveled and the time taken for each set of data points in the table. We can select any two data points to calculate this ratio. Let's use the first and second data points: (2, 90) and (3, 135).
A: Find the constant of proportionality:
The ratio of distance to time for the first set of data points is: 90/2 = 45.
For the second set of data points, the ratio is: 135/3 = 45.
Since both ratios are equal, we can conclude that the constant of proportionality is 45.
B: Use the constant of proportionality to write a unit rate for the data in the table:
The unit rate is the ratio of distance to time when the time is 1 hour. Since we know the constant of proportionality is 45, we can use it to calculate the unit rate.
Therefore, the unit rate for the data in the table is 45 miles per hour.
C: Write an equation to represent the relationship between time, t, and distance, d:
In this case, since the constant of proportionality is given, we can write the equation as:
d = k * t
Where:
d represents the distance
k represents the constant of proportionality
t represents the time taken
Substituting the value of the constant of proportionality found in part A, which is 45, into the equation, we get:
d = 45 * t
Therefore, the equation representing the relationship between time, t, and distance, d, is d = 45t.