Question

Use the table to answer the following questions.

Time (hours) Distance (miles)
2 90
3 135
5 225
6 270
1.Find the constant of proportionality.

2.Use the constant of proportionality to write a unit rate for the data in the table.

3.Write an equation to represent the relationship between time, t, and distance, q

Answer 1

1. The constant of proportionality is 45, which can be found by dividing any distance by its corresponding time:

90 ÷ 2 = 45
135 ÷ 3 = 45
225 ÷ 5 = 45
270 ÷ 6 = 45

2. The unit rate for this data is 45 miles per hour, which is the constant of proportionality.

3. The equation to represent the relationship between time, t, and distance, q, is:

q = 45t

This means that the distance traveled is equal to 45 times the time elapsed. It is a linear equation with a slope of 45.

Answer 2

Use the constant of proportionality to write a unit rate for the data in the table. And write an equation to represent the relationship between time, t, and distance, d.

Answer 3

The constant of proportionality is 45, as determined in the previous question.

1. The unit rate for this data is 45 miles per hour, which represents the rate at which distance changes with respect to time.

2. The equation to represent the relationship between time, t, and distance, d, is:

d = 45t

This means that the distance traveled is equal to 45 times the time elapsed. It is a linear equation with a slope of 45.