Question 413507: The linear function determines the exchange between the Dollar and the Yen. If in 1990 a dollar was worth 125 yens and in 2010 a dollar is worth 80 yen how many yens will a dollar be worth in 2015 according to this model?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! in 1990 a dollar was worth 125 yen.
in 2010 a dollar is worth 80 yen.
your equation is in the form of y = mx + b where m is the slope and b is the y-intercept.
x represents the year
y represents yen per dollar.
if we subtract 1990 from the year, then x = 0 represents 1990 and x = 20 represents 2010
m is the slope.
x1,y1 = 0,125
x2,y2 = 20,80
m is equal to (y2-y1) / (x2-x1) = (80-125) / (20-0) = -45/20 = -9/4
your equation is now y = (-9/4)x + b
to find b, substitute either one of the points in the equation and solve for b.
we'll use x1,y1 = 0,125
substituting in the equation, we get:
125 = 0 + b
this makes b = 125
your equation now becomes y = (-9/4)x + 125
in 2015, x will be equal to 2015 - 1990 = 25
substitute 25 for x in the equation to get:
y = (-9/4)*25 + 125 = - 56.25 + 125 = 68.75
in 2015, the dollar will be worth 68.75 yen at the projected straight line rate.
a graph of this equation is shown below:
A horizontal line at y = 125 intersects the graph of the equation at x = 0 which is the same as 1990.
A horizontal line at y = 80 intersects the graph of the equation at x = 20 which is the same as 2010.
A horizontal line at y = 68.75 intersects the graph of the equation at x = 25 which is the same as 2015.
The answer is that, in 2015, the dollar will be worth 68.75 yen.
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