Final answer:
To find a point on a line using two given points, calculate the slope using the coordinates of these points, write the linear equation in slope-intercept form, then substitute any x value to find the corresponding y value, and use a calculator for precision.
Step-by-step explanation:
To find a point on a line given two points, we can use the linear equation derived from those points. Initially, one should choose two points that are far apart on the line to minimize potential errors in calculation. The chosen points provide us with x and y values to calculate the slope of the line, which is the rate of change of y with respect to x. For example, if the points (6.4 s, 2000 m) and (0.50 s, 525 m) are given, we first calculate the slope (m) with the formula m = (Y₂ - Y₁) / (X₂ - X₁), where (X₁, Y₁) and (X₂, Y₂) represent the two chosen points.
After calculating the slope, we can then use either point to write the linear equation by substituting the x and y values into the slope-intercept form (y = mx + b) and solve for the y-intercept (b). Once the equation is found, we can substitute any x value into this equation to find the corresponding y value, hence locating a new point on the line.
Finally, the complete linear equation can be entered into a calculator or computer to get precise results, preferably rounded to four decimal places. By following these steps, we can efficiently use a calculator to determine new points on a line given two points.