function rule for tis
points- 1 2 3 4
lines- 0 1 3 6
its similar to an earlir one i posted but i still don't quite understand
thanks
it deals with the number of points that a certain number of lines drawn have.
BTW, I think you have your headings backwards,
the first set of numbers should be lines,
the second set of numbers are the number of intersection points those lines have
e.g.
1 line has no intersections points
2 lines have one intersection points
3 lines have 3 intersection points
4 lines have 6 intersection points
etc.
can you see a pattern here?
yeaa i understand and can see the patterns i just don't know how to find the function the way you did...
I don't know what grade level you are in, so I can't guess how sophisticated the method should be that I describe.
suppose we double your second line from
0 1 3 6 ... to
0 2 6 12 ...
notice that those are like
1x0, 2x1, 3x2, 4x3 .... or n(n-1)
but we multiplied our original numbers by 2, so let's divide our formula by 2 to get back to the originals.
so the function rule would be
number of points = n(n-1)/2 , where n is the number of lines drawn.
testing:
If I had 4 lines drawn, n=6
and no. of intersection points is (6x5)/2 = 15
In order to find the function rule for the given points and lines, we need to determine the relationship between the number of points and lines. Let's analyze the given data:
Points: 1 2 3 4
Lines: 0 1 3 6
From the information provided, we can see that when there is 1 point, there are 0 lines. When there are 2 points, there is 1 line. When there are 3 points, there are 3 lines, and when there are 4 points, there are 6 lines.
To find the function rule, we need to determine the pattern or relationship between the number of points and lines. In this case, we can notice that the number of lines is increasing as the number of points increases. Let's calculate the difference between consecutive numbers in the lines column:
1 (line value for 2 points) - 0 (line value for 1 point) = 1
3 (line value for 3 points) - 1 (line value for 2 points) = 2
6 (line value for 4 points) - 3 (line value for 3 points) = 3
The differences between consecutive line values are increasing by 1 each time. This indicates that the relationship between points and lines is quadratic.
Now, let's write an equation for this quadratic relationship. We can assume that the equation is in the form of y = ax^2 + bx + c, where y represents the number of lines and x represents the number of points.
Using the points we have, we can substitute the values and form a system of equations:
When x = 1, y = 0:
0 = a(1)^2 + b(1) + c ----> equation (1)
When x = 2, y = 1:
1 = a(2)^2 + b(2) + c ----> equation (2)
When x = 3, y = 3:
3 = a(3)^2 + b(3) + c ----> equation (3)
Let's solve this system of equations to find the values of a, b, and c.