Answer:
y = .25x + 2.5
Step-by-step explanation:
First find the slope which is m in y = mx + b. y = mx + b is the standard form for a line.
m = (y₂-y₁)/(x₂-x₁)
m = (3-1)/(2+6)
m = 2/8
m = 1/4
Plug that in.
y = 1/4x + b
To find b plug in one of the two points and solve.
3 = 1/4(2) + b
3 = 1/2 + b
3 - 1/2 = 1/2 - 1/2 + b
2.5 = b
The relation is that the diameter is twice the length of the radius.
To make more proof, look at the attached image below.
There would be 12 people at the party!
In general, with n+1 people, the number of handshakes is the sum of the first n consecutive numbers: 1+2+3+ ... + n.
Since this sum is n(n+1)/2, we need to solve the equation n(n+1)/2 = 66.
This is the quadratic equation n2+ n -132 = 0. Solving for n, we obtain 11 as the answer and deduce that there were 12 people at the party.
Since 66 is a relatively small number, you can also solve this problem with a hand calculator. Add 1 + 2 = + 3 = +... etc. until the total is 66. The last number that you entered (11) is n.
Hope this helps!
