(0,0) (20,7.2) (40,12.8) (60,16.8) (80,19.2) (100,20.0) (120,19.2) (140,16.8) (160,12.8)

how do you find the equation curve of best fit with these numbers

To find the equation of the curve that best fits these data points, you can use a method called "curve fitting" or "regression analysis." There are different types of regression analysis, and one commonly used method is called "linear regression." Linear regression assumes that the relationship between the variables can be modeled by a linear equation.

Here are the steps to find the equation of the best-fit curve using linear regression:

1. Plot the given data points on a graph with the x-axis representing the independent variable and the y-axis representing the dependent variable.

2. Inspect the plotted data points to determine if they form a linear pattern or if they appear to follow a different type of curve. If the data points roughly follow a straight line, linear regression may be appropriate. Otherwise, you may need to consider using a different type of regression analysis, such as polynomial regression or exponential regression.

3. Using linear regression, we assume that the equation of the best-fit line can be represented by:
y = mx + b

Here, "m" represents the slope of the line, and "b" represents the y-intercept.

4. To find the equation of the best-fit line, you need to calculate the values of "m" and "b." This can be done using various statistical methods, such as the least squares method.

5. Once you have the values of "m" and "b", substitute them into the equation y = mx + b to obtain the equation of the best-fit line.

To perform these calculations, you can use software like Microsoft Excel, Google Sheets, or various statistical analysis tools. These tools have built-in capabilities for performing linear regression analysis and will provide you with the equation of the best-fit line.

Alternatively, if you have programming knowledge, you can use programming languages like Python or R to perform the calculations and find the equation of the best-fit line using libraries such as NumPy or scikit-learn.