Final answer:
To find the equation of a line through two points, calculate the slope using the change in y divided by the change in x, then use the point-slope form of the equation to construct the full equation.
Step-by-step explanation:
To find the equation of a line passing through two points, you need to determine two things: the slope of the line and the y-intercept, if necessary. The slope (m) is calculated by finding the change in y-coordinates divided by the change in x-coordinates between the two points, which is ∆y/∆x = (y2 - y1)/(x2 - x1).
For example, for the points (0,0) and (2,1), the slope is calculated as (1 - 0)/(2 - 0) = 1/2. Now that we have the slope and one point, we can use the point-slope form of a line which is y - y1 = m(x - x1). Substituting our values we get y - 0 = (1/2)(x - 0), which simplifies to y = 1/2x, the equation of the line passing through these points.
In MCQ format, if the options provided correspond to the slopes of the lines passing through the given points, you would calculate the slope as described above for each pair of points and pick the option that matches your calculation. If a full equation of a line is requested in MCQ format, you would use the method described to find the correct equation and choose the corresponding option.