Time Spent on the Internet
By: Rida Bukhari
Table of Values for Bob and Lisa
Equations for Both
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
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
Finding 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).