Final answer:
The equation of a tangent line to a curve at a certain point is found by first calculating the slope of the curve at that point. The provided solution involves finding two endpoints of the tangent line, calculating the slope as the average rate of change between these points, and then using the point-slope form to write the tangent line's equation.
Step-by-step explanation:
When finding the equation of a tangent line to a curve at a specific point, we first need to determine the slope of the tangent. The slope of a curve at a given point can be found using the derivative of the curve's equation at that point. However, since the question contains a typo or some irrelevant parts, we'll refer to the provided steps.
In the given steps, the slope (v) of the tangent line is found by taking two endpoints of the tangent at different times (t) and positions (m). To find the slope v, you would subtract the initial position from the final position (3120 m - 1300 m) and then divide that by the change in time (32 s - 19 s). This would give you the average velocity over that interval, which is the slope of the tangent line at t = 25 s.
Using the slope and one of the points on the line, you could then form the equation of the tangent line using the point-slope form of a linear equation, y - y1 = m(x - x1), where m is the slope and (x1, y1) is one of the given points.