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
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.
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.
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.
To find the constant of proportionality, you can take any two sets of values from the table and divide the distance by the time. Let's choose the first set of values: (2, 90).
1. Constant of Proportionality:
D1 / T1 = 90 / 2 = 45
The constant of proportionality is 45.
2. Unit Rate:
The unit rate is found by dividing the distance by the time. In this case, the unit rate is:
45 miles per hour
3. Equation:
To represent the relationship between time, t, and distance, q, we can write the equation using the constant of proportionality:
q = 45t
where q is the distance in miles and t is the time in hours.