It is appropriate to model data with a linear function when there is a linear relationship between the variables being analyzed. In this case, a linear function can accurately represent the trend and pattern of the data.
An example of real-world data that can be modeled with a linear function is the relationship between the number of hours worked and the earnings of an employee. Let's consider a scenario where an employee earns a fixed hourly wage.
Here is a sample of the data representing the relationship between the number of hours worked and earnings:
Number of Hours Worked (x): [10, 20, 30, 40, 50]
Earnings (y in dollars): [100, 200, 300, 400, 500]
To model this data with a linear function, we can use the equation y = mx + b, where y represents the earnings, x represents the number of hours worked, m represents the slope of the line, and b represents the y-intercept.
To find the values of m and b, we can use the formula: m = (y2 - y1) / (x2 - x1) and then substitute the values from the data into the formula.
Taking the first two data points: (x1, y1) = (10, 100) and (x2, y2) = (20, 200):
m = (200 - 100) / (20 - 10) = 10
Now, to find b, we can substitute one of the points into the equation y = mx + b. Let's use the first data point, (10, 100):
100 = 10(10) + b
100 = 100 + b
b = 0
Therefore, the linear function representing this data would be:
Earnings = 10 * Number of Hours Worked
This equation accurately models the relationship between the number of hours worked and earnings in this scenario.
Throughout this unit, you will participate in a discussion based on the following question:
When is it appropriate to model data with a linear function? Give an example of real-world data that can be modeled with a linear function. Include the linear function and a sample of the data. my example would be a car payment, make it really simple
1 answer
1 answer