Question 90923
Disease 1985 1990 1995 2002 
Heart Disease 771169 720058 737563 696,947 
Cancer 461563 505322 538445 557,271 

1. 
a. Plot this data for each disease as points in a rectangular coordinate system.
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On an xy-coordinate system plot the four points you are given for heart
disease deaths and four points for cancer deaths:
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Let 1985 be 0, 1990 be 5, 1995 be 10, 2002 be 17
Heart Disease Points: (0,771169),(5,720058),(10,737563),(17,696,947)
Cancer DiseasePoints: (0,461563),(5,505322),(10,538445),(17,557,271) 
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b. Using a smooth line, connect your data points for each disease.
You should get two line segments: one for heart disease and one for cancer.
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c. On a separate graph, plot only the years 1985 and 2002 and connect the points with a straight line. 
Do that
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d. Calculate the slope of each line. 
Heart Disease Points: (0,771169),(5,720058),(10,737563),(17,696,947)
Cancer DiseasePoints: (0,461563),(5,505322),(10,538445),(17,557,271) 
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To get the slope look at the 1st and 4th points. The slope of the change
in the y-values divided by the change in the x values, as follows:
Heart slope: [696947-771169)/[17-0] = -4366
Cancer slope: [557271-461563]/[17-0] = 95708
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e. Write the equation of each line in the slope-intercept form.
We have the slope but need the y-intercept.  The y-intercept is the 
y-value associated with x=0,  
For the heart data the y-intercept is 771169; for the cancer data the 
y-intercept is 461563
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Having the slope and the y-intercept for each set of data we can write
the equation for each.
Heart equation: y = -4366x + 771169
Cancer equation: y = 95708x + 461563
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f. Using the equations of each line, make a reasonable prediction as to the number of deaths we might expect in 2005 due to each of these medical conditions.
Since 2005 is 20 years after 1985, let x = 20 and solve for y in each equation.
Heart equation: y = -4366x + 771169
y = -4366*20+771169
y = 683,849 deaths from heart disease in the year 2005
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Cancer equation: y = 95708x + 461563
y = 95708*20 + 461563 
y = 2,375,723 deaths from cance in the year 2005
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2. Please include a response to this two part follow-up question with your submission.
a. Can the graphs that you constructed be classified as functions? Explain.
Yes because for each year there is one number of deaths from each cause.
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b. Why is it reasonable that negative numbers are excluded from both the domain and the range of each of the disease graphs? What would the real-world implications be if these numbers were actually part of the domain and/or range?
Negative Domain would imply years before 1985
Negative Range would imply negative number of deaths which is meaningless.
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Cheers,
Stan H.