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.
can someone please help me a tutor or someone I need to get the last quiz don't for a big grade
welll that doesn't help does it?
A. 45
here is a trick that my tutor taught me.. y/x = miles /hours which means that if i divide 90 by 2, 135 by 3, 225 by 5, 270 by 6 i get 45
a. To find the constant of proportionality, we need to determine how the distance changes in relation to time. We can choose any two points from the table. Let's use the points (2, 90) and (3, 135).
The constant of proportionality is found by dividing the change in distance by the change in time.
Change in distance = 135 - 90 = 45 miles
Change in time = 3 - 2 = 1 hour
So, the constant of proportionality is 45 miles per hour.
b. To write a unit rate for the data in the table using the constant of proportionality, we simply express the rate of change in distance per unit of time.
The unit rate is 45 miles per hour. This means that for every hour that passes, the distance traveled will be 45 miles.
c. To write an equation representing the relationship between time, t, and distance, d, we can use the constant of proportionality.
The equation can be written as:
d = 45t
Here, d represents the distance in miles and t represents the time in hours. The equation states that the distance traveled is equal to the constant of proportionality (45) multiplied by the time (t).