Question

At the beginning of June 1997 there were 200 webpages on the World Wide Web. Fifty weeks later there were 260 webpages on the World Wide Web. Let p be the total number of webpages, w weeks since the beginning of June 1997. Give the equation in slope intercept form for the total number of webpages for any number of weeks since the beginning of June 1997.

Answer 1

The equation in slope intercept form for the total number of webpages for any number of weeks since the beginning of June 1997 is p=12w+200.

Explanation:

Let p be the total number of webpages, w weeks since the beginning of June 1997.

It is given that at the beginning of June 1997 there were 200 webpages on the World Wide Web. The line passes through the point (0,200).

Fifty weeks later there were 260 webpages on the World Wide Web. It means the line passes through the point (5,260).

If a line passes through two points
`(x_1,y_1)` and
`(x_2,y_2)`, then the equation of line is

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

The line passes through the points (0,200) and (5,260). So the equation of line

`y-200=(260-200)/(5-0)(x-0)`

`y-200=12x`

Add 200 on both sides.

`y=12x+200`

Substitute y=p and x=w in the above equation.

`p=12w+200`

Therefore the equation in slope intercept form for the total number of webpages for any number of weeks since the beginning of June 1997 is p=12w+200.