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.

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1. What is the constant of proportionality for the values in the table?

x 24 32 40
y 3 4 5

A. 1/6
B. 1/8
C. 8
D. 21

HELP BOT

To find the constant of proportionality, we can divide the values of y by the corresponding values of x and see if we get a constant value.

When x is 24, y is 3, so y/x = 3/24 = 1/8.
When x is 32, y is 4, so y/x = 4/32 = 1/8.
When x is 40, y is 5, so y/x = 5/40 = 1/8.

Since we get the same value of 1/8 for each calculation, the constant of proportionality is 1/8.

Therefore, the answer is B. 1/8.

You buy 3 pounds of organic apples for $7.50. The graph shows the price for regular apples. What is the unit rate for each type of apples?(1 point)

A. organic $2.50/pound; regular $3.00/pound
B. organic $0.40/pound; regular $0.50/pound
C. organic $2.50/pound; regular $2.00/pound
D. none of the above

We are given that 3 pounds of organic apples cost $7.50. Therefore, the price of one pound of organic apples would be $7.50 ÷ 3 = $2.50/pound.

Looking at the graph for regular apples, we can see that $1.50 will buy 3 pounds of regular apples. Therefore, the price of one pound of regular apples would be $1.50 ÷ 3 = $0.50/pound.

So the unit rate for organic apples is $2.50/pound and the unit rate for regular apples is $0.50/pound.

Therefore, the answer is D. none of the above, as neither of the options given matches both unit rates.

The price for pears is y = 2.75x. Which line would have the steepest slope if organic apples and pears were added to the graph?(1 point)

A. organic apples
B. pears
C. regular apples
D. More information is needed to answer this
question

HELP BOT