Question

What is the constant of proportionality? Write an equation that relates the number of pages read (y) to the length of time in hours spent reading. (x)

Answer 1

Answer/Step-by-step explanation:

Constant of proportionality is given as
`k = (y)/(x)`. Where k is the constant of proportionality, y = number of pages read while x is the corresponding time taken to read the pages.

Constant of proportionality will be the same for each given pair on the table. We can take any pair to find k.

`k = (52)/(2)`

`k = 26`

Constant of proportionality = 26

The relationship between number of pages read and time taken is a proportional relationship, hence, the equation that describes this relationship would be:

`y = kx`

Substitute the value of k into the equation

`y = 26x`

This equation represents the relationship, and hence can be used to complete the missing values of the table as shown below:

Length of time (x) ==> no of pages read (y)

3 ==>
`y = 26x = 26(3) = 78`

156 = 26x; x = 156/26 = 6 ==> 156

8 ==>
`y = 26x = 26(8) = 208`

234 = 26x; x = 234/26 = 9 ==> 234