Final answer:
To find a function for a line, calculate the slope using two points and the y-intercept. Inputting data into a calculator and using the regression function helps find the least-squares regression line, representing the best-fit line for a data set.
Step-by-step explanation:
To find a function that describes a line passing through specific points, you need to determine the slope and y-intercept of the line. This can be achieved through several methods, including the median-median approach, calculating the mean of the x and y values, or using the least-squares regression line. For example, if you have two points on a line and you want to calculate the slope, you would use the formula (Y₂ - Y₁) / (X₂ - X₁) where the Y and X values represent the y and x coordinates of the two points, respectively.
Once you have the slope, you can use the y-intercept to write the equation of the line in the form y = mx + b, where m is the slope and b is the y-intercept. If you have technology, like a graphing calculator, you can enter the data, make a scatter plot, and utilize the calculator’s regression function to obtain the equation of the least-squares regression line, which is typically the best fit for the data. This line can then be added to your scatter plot.
For example, the lines Y2 = -173.5 + 4.83x − 2(16.4) and Y3 = -173.5 + 4.83x + 2(16.4) suggest modifications to the line of best fit, y = -173.5 + 4.83x, by shifting it up or down. These lines have the same slope as the original line of best fit but differ in their y-intercept, which is adjusted by ±2(16.4).