Final answer:
To calculate the equation of a line, determine the slope (rise over run) between two points and use this slope with one of the points to write the line's equation. Online calculators greatly simplify finding the equation and plotting data. TI-83, TI-83+, and TI-84+ calculators have specific functions for plotting and regression analysis.
Step-by-step explanation:
To calculate the equation of a line passing through two points, you will need to determine the slope of the line, which can be found using the formula for slope (m): m = (Y₂ - Y₁) ∕ (X₂ - X₁), where (X₁, Y₁) and (X₂, Y₂) are the coordinates of the two points.
After calculating the slope, use one of the points and the slope in the point-slope form of the equation of a line: y - Y₁ = m(x - X₁) to find the specific line equation. This can be transformed into slope-intercept form: y = mx + b, if desired.
Online calculators can simplify this process. Simply enter your two points and it will output the linear equation, often with options to round to a desired number of decimal places. Additionally, you can make a scatter plot and use the calculator's regression function to find the least-squares regression line, providing the best fit for data that may not fall perfectly in a line.
For TI-83, TI-83+, and TI-84+ calculator users, instructions are available to help calculate the best-fit line and create a scatter plot, which is particularly useful in a classroom or homework setting to visualize the correlation between the data points.