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,

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) (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

Start with the slope formula.

Plug in , , , and

Subtract from to get

Subtract from to get

Reduce

So the slope of the line that goes through the points

and

is

Now let's use the point slope formula:

Start with the point slope formula

Plug in , , and

Distribute

Multiply

Add 51 to both sides.

Combine like terms.

Simplify

So the equation that goes through the points

and

is

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