Final answer:
To find the equation of a line, enter the data points into a calculator, create a scatter plot, and use the regression function to obtain the least-squares regression line, rounding the resulting equation to four decimal places.
Step-by-step explanation:
To find the equation of a line that passes through two points, you need to use these steps:
- Enter the data into a calculator and use it to make a scatter plot.
- Utilize the calculator's regression function to find the equation of the least-squares regression line. This line minimizes the sum of the squares of the vertical distances of the points from the line.
- Once the equation is obtained from the calculator, you can round it to four decimal places.
If you are working with only two points and want to find the equation of a line directly, you can use the formula for the slope (m) which is (Y2 - Y1) / (X2 - X1), where Y2 and Y1 are the y-values of the two points on the line, and X2 and X1 are the x-values. Then, use the slope and one of the points to find the equation of the line in the form y = mx + b, where m is the slope and b is the y-intercept.
For example, let's say the calculated regression equation using the calculator's function is y = -173.5 + 4.83X. To graph this best-fit line, you would type this equation into the Y= section of a graphing calculator and view the plot.