in 1979, the death rate,D, from acute myocardial infarction for people between the ages of 65 and 74 years was 577 per 100,000 people. In 1996, the rate was 262 deaths per 100,000 people. Round to one decimal place in part a. write sentences for your answer in part b and c.

a.if t is the # of years since 1970, write a linear equation that gives the # of deaths per 100,000 from acute myocardial infarction in year t.
b. estimate the death rate in 1990.
c. in what year will the death rate be 114 deaths per 100,000.

a. To find a linear equation that gives the number of deaths per 100,000 from acute myocardial infarction in year t, we can use the given data points (1979, 577) and (1996, 262).

First, we need to find the slope of the line, which represents the change in death rate per year. The slope, m, can be calculated using the formula:

m = (y2 - y1) / (x2 - x1)

Substituting the values, we have:

m = (262 - 577) / (1996 - 1979)
m = -315 / 17

Next, we can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

Choosing the point (1979, 577), we have:

y - 577 = (-315 / 17)(x - 1979)

This equation gives the number of deaths per 100,000 from acute myocardial infarction in year t.

b. To estimate the death rate in 1990, we need to substitute the year 1990 into the linear equation we obtained in part a.

Plugging in x = 1990, we have:

y - 577 = (-315 / 17)(1990 - 1979)

Simplifying this equation will give us an estimate of the death rate in 1990.

c. To find the year when the death rate will be 114 deaths per 100,000, we can use the linear equation found in part a.

Substituting y = 114 into the equation and solving for x will give us the year, t.

114 - 577 = (-315 / 17)(x - 1979)

Solving this equation for x will give us the year when the death rate will be 114 deaths per 100,000.