SOLUTION: In 1945, when the United Nations was formed, there were 51 member nations. In 1987, there were 159 member nations. Write an equation that gives the number of nations in the UN, y,

Algebra ->  Equations -> SOLUTION: In 1945, when the United Nations was formed, there were 51 member nations. In 1987, there were 159 member nations. Write an equation that gives the number of nations in the UN, y,       Log On


   

Question 170856: In 1945, when the United Nations was formed, there were 51 member nations. In 1987, there were 159 member nations. Write an equation that gives the number of nations in the UN, y, in terms of the year, t. Let t=0 correspond to 1945 and assume that membership followed a linear pattern.
Do I start by making two points? (51,0) (159,42) ?? Help
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
You're on the right track. However, you have the coordinates of the points mixed up. Think of it like this: "t" is the independent and "y" is the dependent variable. Why is "t" the independent variable? Since the time can be any positive value (which is NOT affected by the number of nations), this means that "t" is independent. Since "y" changes as "t" changes, this means that "y" is dependent on "t"


Remember, any point on a coordinate system follows the form

(independent variable, dependent variable)


So this means that every point is in the form (t,y)


This means that the two points are really (0,51) and (42, 159)



So let's find the equation of the line through the points (0,51) and (42, 159)


---------------------------------------




First let's find the slope of the line through the points and


m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula.


m=%28159-51%29%2F%2842-0%29 Plug in y%5B2%5D=159, y%5B1%5D=51, x%5B2%5D=42, and x%5B1%5D=0


m=%28108%29%2F%2842-0%29 Subtract 51 from 159 to get 108


m=%28108%29%2F%2842%29 Subtract 0 from 42 to get 42


m=18%2F7 Reduce


So the slope of the line that goes through the points and is m=18%2F7


Now let's use the point slope formula:


y-y%5B1%5D=m%28x-x%5B1%5D%29 Start with the point slope formula


y-51=%2818%2F7%29%28x-0%29 Plug in m=18%2F7, x%5B1%5D=0, and y%5B1%5D=51


y-51=%2818%2F7%29x%2B%2818%2F7%29%28-0%29 Distribute


y-51=%2818%2F7%29x%2B0 Multiply


y=%2818%2F7%29x%2B0%2B51 Add 51 to both sides.


y=%2818%2F7%29x%2B51 Combine like terms.


y=%2818%2F7%29x%2B51 Simplify


So the equation that goes through the points and is y=%2818%2F7%29x%2B51