Question 283813: GRAPHS AND FUNCTIONS
Please help me identify a situation or problem that could be represented via a graph. Consider the practical application of graphing within the context of health care. Thanks once again.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! The cost of health care 10 years ago was $2,000 per person per year.
The cost of health care today is $4,000 per person per year.
Based on a straight line projection, what do you estimate the cost of health care to be in 20 years?
You let x = the year.
You let y = the cost of health care per person.
x1 = -10 represents 10 years ago
y1 = $2000 represents the cost of health care per person 10 years ago.
you get (x1,y1) = (-10,2000)
x2 = 0 represents today.
y2 = $4000 represents the cost of health care per person today.
you get (x2,y2) = (0,4000)
You need to make an equation that relates health care to the year.
Your equation will be a linear equation of the form y = mx + b
m is the slope and b is the y-intercept (value of y when x = 0).
The slope is given by the formula m = y2-y1 / x2-x1
y2-y1 = 4000 - 2000 = 2000
x2-x1 = 0 - (-10) = 10
your slope is 2000/10 = 200 per year.
your y-intercept is the value of y when x = 0
your equation so far is y = 200*x + b
substitute one of the points (x1,y1) or (x2,y2) for x and y in the equation.
use (x2,y2) = 0, y = 4000
your equation becomes:
4000 = 2000*0 + b
solve for b to get b = 4000
your equation becomes y = 200*x + 4000
graph of this equation is shown below:
I placed horizontal lines at y = 2000, y = 4000, y = 8000
y = 2000 should correspond to the cost of health care 10 years ago. This is when x = -10.
y = 4000 should correspond to the cost of health care today. This is when x = 0.
y = 8000 should correspond to the cost of health care 20 years from now. This is when x = 20.
The points where these horizontal lines intersect with the graph of the equation y = 200*x + 4000 should correspond to x = -10, x = 0, and x = 20. Trace a vertical line down from those intersection points and you should intersect with the x-axis at about those values.
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