Use the tables to answer the following questions.

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.

time distance

(hours) (miles)

2 90

3 135

5 225

6 270

(a) Find the constant of proportionality:

Answer:

What is constant of proportionality?/

Two varying quantities are said to be in a relation if they are connected to each other in a proportion. If they are connected by a constant, this constant c is called constant of proportionality or co-efficient of proportionality.

let 't' be time and 'd' be distance.

At 2 hours, the distance covered is 90 miles 90/2 = 45

At 3 hours, the distance covered is 135 miles 135/3 = 45

and so on ...

Hence the constant of proportionality 'c' is 45.

(b) use the constant of proportionality to write a unit rate for the data in the table.

Answer:

Using the data in the table:

rate of the data is the slope of the graph that is distance/time = velocity.

So, the unit rate of the data means the distance covered per unit time that is the distance in miles covered in per hour is equal to the velocity.

For unit rate, we use the largest values of the data which are

time = 6 hours

distance covered = 270 miles

Unit rate = Velocity = 270/6

= 45 miles per hour.

(c) An equation to represent the relationship between time 't' and distance 'd'.

Answer:

Whenever forming a relational equation between two quantities from a table, follow these steps:

Step 1:

Check if the two relations are directly proportional or inversely proportional.

Step 2:

Use a constant of proportionality to transform the relation into an equation.

In our case, Distance covered increases with the time, so it is directly proportional.

distance ∝ time

Using a constant of proportionality 'c', we get the following equation:

d = ct

Checking if the equation satisfies the table:

90 = c*2

135 = c*3

225 = c*5

270 = c*6

c = 45 satisfies the data in equation d = ct hence the equation satisfies the data.