# Time Spent on the Internet

## The Comparison

Bob and Lisa were active students in high school, and so they spent a lot of time on the Internet. So, they decided to compare the number of hours they spend weekly on the internet, for 3 months.

## Table of Values for Bob and Lisa

After observing their results for 12 weeks, here is what they recorded:

## Equations for Both

For Bob:

To find the equation, first we need to find slope. Since we have sufficient data available, we can use points from the data: (1,4) and (2,6). The formula is y2-y1/x2-x1

m = 6-4 / 2-1

m = 2/1

m = 2

The next step, is to find a value for "b" to complete the equation. This can be done by substituting a point from the data. For example, we can use (2,6)

6 = 2(2) + b

6 = 4 + b

6 - 4 = b

2 = b

Now, since we have slope and the y-intercept, the equation can be formed and it would be: y = 2x + 2

For Lisa:

Similarly, here we also have to find slope first. This will be done using the same method and formula (y2-y1 / x2-x1)

Say we use points, (1,4) and (2,7)

m = 7-4 / 2-1

m = 3 / 1

m = 3

Now, we also have to substitute a point from the data to figure out "b." Say we use, (2,7).

7 = 3(2) + b

7 = 6 + b

7 - 6 = b

1 = b

A formula can now be created, using the data of the slope and the y - intercept, the formula is: y = 3x + 1

## Graph to Show Their Lines & Intersection

Here, is the graph for both Bob and Lisa. The intersection point, (1,4) is circled.

## Finding the Intersection Point

There are a couple different methods that can be used to find the intersection point.

For the first method, all we have to do is look at the graph above, to see where the lines intersect. On the graph, the lines intersect at (1,4). This means that during the 1st week, they both spent 4 hours online.

For the second way, we can substitute equations to help us find the points.

3x + 1 = 2x + 2

3x - 2x = 2-1

x = 1 <-- this gives the x point on the graph.

For the other point, we can use an equation to find it.

y = 3x + 1

y = 3(1) + 1

y = 3 +1

y = 4

Both of these methods show the same thing, that these points will intersect at (1,4).

## Significance of Graph and Intersection

The graph has an overall significance, along with the specific intersection point. Firstly, the graph shows the general trend regarding the amount of time that these two teenagers spend online, it is also evident that as the time goes on, they are spending more time online. Therefore, the significance of the graph is that it can be used to predict future trends. Furthermore, the intersection point has the significance of showing where they meet in their data, which happens during the first week. It also shows that after this point the two teens completely changed the amount of time each was spending, and they went their separate ways.

## Conlcusion

In conclusion, these teens are spending more time on the internet per week, as time goes on. It is during the first week where they intercept, during which time, they both spend 4 hours on the internet.