Final answer:
To find the standard form of a line using two points, calculate the slope using the formula (Y₂ - Y₁) / (X₂ - X₁) for accuracy. Input the data into a calculator, create a scatter plot, and apply the regression function to derive the line's equation, rounding to four decimal places when needed.
Step-by-step explanation:
To determine the standard form of a line given two points, first, choose two widely separated points for accuracy. Use the points to calculate the slope, which is constant for a straight line. Let's use the example points (6.4 s, 2000 m) and (0.50 s, 525 m). The general formula for slope (m) is given by:
m = (Y₂ - Y₁) / (X₂ - X₁)
After calculating the slope, the next step is to enter the data into a calculator, plot a scatter plot, and use the regression function to find the equation of the least-squares regression line. This equation can be rounded to four decimal places for precision. An example solution provided was y = −3204 + 1.662x, representing the equation of the line of best fit on a scatter plot.
Analyze the Data by entering it into a graphing calculator or computer software to determine the line's equation, ensuring to verify it through visualization with a scatter plot and adding the regression line for comparison.