having trouble making an equation for a word problem

Question

The number of volunteers of a worldwide organization has increased 5.2 million in 2002 to 11.5 million in 2010.

 

Find an equation for the line containing the given points. Let x represent the number of years after 2000 and y the number of volunteers in millions. Type equation in slope intercept form.

I think X would be 13 years and y would be the additional 6.3 million then I get lost

Then estimate the number of volunteers in 2005 and 2013

Answer 1

The slope-intercept form of a straight line is y = mx + b, where m is the slope and b is the y-intercept.  Let x = the number of years since 2002 and let y = the number of volunteers measured in millions.  We have two points ((x,y)) on the line:

 

(2002,5.2)

(2010,11.5)

 

The slope is the change in the y-coordinate between the two points over the change in the x-coordinate:

 

m = (11.5-5.2) / (2010-2002) = 6.3/8 = 0.7875 millions per year

 

Since we are starting from 2002, the y-intercept is 5.2 million.

 

y = (0.7875)x + 5.2   measured in millions of volunteers

 

To estimate the number of volunteers in 2005, enter x = 2005-2002 = 3 into the equation and compute the corresponding y (number of volunteers in millions).  For 2013, enter x = 2013-2002 = 11.