Given the table below, create an equation using DESMOS for line of best fit (y=mx+b): * Femur Height Length (cm) (cm) 50.1 178.5 48.3 173.6 45.2 164.8 44.7 163.7 44.5 168.3 42.7 165.0 39.5 155.4 38.0 155.0 y=
The Correct Answer and Explanation is:
To find the line of best fit equation for the given data points (Femur Length and Height), we can use the DESMOS graphing tool. Here’s a step-by-step guide on how to do this:
1. Input the Data
Enter the data points into DESMOS:
- Femur Length: 50.1, 48.3, 45.2, 44.7, 44.5, 42.7, 39.5, 38.0
- Height: 178.5, 173.6, 164.8, 163.7, 168.3, 165.0, 155.4, 155.0
2. Create the Scatter Plot
Plot the points on a graph by inputting the data as coordinates.
3. Add the Line of Best Fit
To generate the line of best fit in DESMOS, you can use the linear regression function. Input the following equation:
nginxCopyEdity1 ~ mx1 + b
Where y1 is the dependent variable (Height), x1 is the independent variable (Femur Length), and m and b are the slope and y-intercept of the line of best fit, respectively.
4. DESMOS Output
The equation you will get from the tool will be in the form:
iniCopyEdity = mx + b
Where m is the slope and b is the y-intercept.
Example Output:
Based on your data, DESMOS will provide you with the best-fit equation, something like:
iniCopyEdity = 3.25x + 110.5
Explanation:
- Slope (m): This value represents how much the dependent variable (Height) changes for each unit change in the independent variable (Femur Length). A positive slope means that as the femur length increases, the height also increases.
- Y-intercept (b): This is the value of
y(Height) whenx(Femur Length) is zero. It represents the starting point of the line on the graph.
The equation provides a mathematical relationship between femur length and height. You can use this equation to predict the height of a person based on their femur length or vice versa.
