Answer/Step-by-step explanation:
Constant of proportionality is given as [tex] k = \frac{y}{x} [/tex]. 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.
[tex] k = \frac{52}{2} [/tex]
[tex] k = 26 [/tex]
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:
[tex] y = kx [/tex]
Substitute the value of k into the equation
[tex] y = 26x [/tex]
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 ==> [tex] y = 26x = 26(3) = 78 [/tex]
156 = 26x; x = 156/26 = 6 ==> 156
8 ==> [tex] y = 26x = 26(8) = 208 [/tex]
234 = 26x; x = 234/26 = 9 ==> 234
