Final answer:
To determine the equation of the line passing through two given points, calculate the slope using the coordinates, then apply the point-slope form of the equation.
Step-by-step explanation:
To find the equation of the line passing through the given points (at12, 2at1) and (at22, 2at2), we first determine the slope of the line.
Since the slope is given by the change in y-coordinates over the change in x-coordinates, we calculate it using the formula (Y2 - Y1) / (X2 - X1). Substituting the respective coordinates, we get (2at2 - 2at1) / (at22 - at12). After finding the slope, we can use the point-slope form of the line, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is one of the given points. Substituting our slope and one of the points into this formula will give us the equation of the straight line.