I need to write a linear function using the following data:
Year Life Expectancy In Years
1940 62.5
1950 71.1
1960 73.1
1970 74.7
1980 77.5
1990 78.8
I know the formula is y=mx+b but im not sure how to determine that from what I have been given.
Thanks for the help!!
first, check the differences:
8.6
2.0
1.6
2.8
1.3
Doesn't look good, since there's no obvious slope. Is this a class in statistics, where you cover linear regression? The 62.5 looks like an outlier.
To write a linear function using the given data, you can use the formula y = mx + b, where y represents the dependent variable (life expectancy in this case), x represents the independent variable (year), m represents the slope or rate of change, and b represents the y-intercept.
To determine the values of m and b, you can use the following steps:
Step 1: Choose two data points from the given data.
Let's choose the points (1940, 62.5) and (1990, 78.8).
Step 2: Calculate the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are the chosen data points.
Substituting the values, we have:
m = (78.8 - 62.5) / (1990 - 1940)
m = 16.3 / 50
m = 0.326
So, the slope (m) is approximately 0.326.
Step 3: Calculate the y-intercept (b) using the formula:
b = y - mx
where (x, y) represents one of the chosen data points.
Substituting the values from (1990, 78.8) and the calculated slope, we have:
b = 78.8 - (0.326 * 1990)
b = 78.8 - 648.74
b ≈ -569.94
So, the y-intercept (b) is approximately -569.94.
Step 4: Write the linear function using the values of m and b:
y = 0.326x - 569.94
Therefore, the linear function representing life expectancy in years as a function of the year is y = 0.326x - 569.94.