In 1992 the life expectency of males in a certain counrty was 73.4 years. In 1999 it was 76.7 years. Let E represent the life expectancy in years t and let t represent the number of years since 1992.
Are we to assume that the increase follows a linear function, i.e., it can be expressed by a straight line graph?
if so, then
treat your data as two ordered pairs
(0,73.4) and (7,76.7)
slope = (76.7-73.4)/(7-0) = 3.3/7 = 33/70
so y = (33/70)t + b
but (0,73.4) is the y-intercept or b
so y = (33/70)t + 73.4
here from 2021
To find the equation that represents the relationship between the life expectancy (E) and the number of years since 1992 (t), we can use the given data points:
In 1992, the life expectancy (E) is 73.4 years. This means that when t = 0 (since it's the number of years since 1992), the life expectancy is 73.4 years.
In 1999, the life expectancy (E) is 76.7 years. This means that when t = 7 (1999 - 1992 = 7), the life expectancy is 76.7 years.
To find the equation of a line, we can use the slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept.
First, let's find the slope (m). The slope (m) represents the change in y divided by the change in x.
Change in y = E2 - E1 = 76.7 - 73.4 = 3.3
Change in x = t2 - t1 = 7 - 0 = 7
m = (Change in y) / (Change in x) = 3.3 / 7
Now, let's find the y-intercept (b). We already know that when t = 0, E = 73.4.
b = E - m * t
= 73.4 - (3.3 / 7) * 0
= 73.4
So the equation that represents the relationship between the life expectancy (E) and the number of years since 1992 (t) is:
E = (3.3 / 7) * t + 73.4