A particular search engine assigns a ranking to a webpage ba

A particular search engine assigns a ranking to a webpage based on the number of links that direct users to the webpage. If no links are found, the webpage is assigned a ranking of 1. If 40 links are found directing users to the webpage, the search engine assigns a page ranking of 5.

Find a linear function that gives the webpage ranking based on the number of links that direct users to it.

How many links will be needed to obtain a page ranking of 7?

Solution

According to question,

We have the Coordinates for the graph.

(0,1) and (40,5)

where, x -> web links, and y -> ranking

Lets find the slope of the equation , using the coordinates

m = y2-y1/x2-x1

=> m = (5-1)/(40-0) = 4/40 = 1/10 = 0.1

=> m = 0.1

Now, lets use the slope intercept form of the equation,

y = mx + b

here m = 0.1 and b = 1, because x is 0 at y = 1

=> y = 0.1 x + 1

Now, lets work on the second part of the question,

How many links will be needed to obtain a page ranking of 7

lets plug y = 7 in the equation, to find x

7 = 0.1 x + 1

Subtract 1 from both the sides

6 = 0.1 x

divide both the sides by 0.1

=> x = 6/0.1

=> x = 60

Therefore, for 60 links the page ranking will be 7.