Final answer:
The point-slope form of a line between the two points (1,2) and (3,5) is y - 2 = (3/2)(x - 1).
Step-by-step explanation:
The point-slope form of a line between the two points (1,2) and (3,5) is given by the equation y - y1 = m(x - x1), where (x1, y1) are the coordinates of the first point and m is the slope of the line.
First, let's find the slope of the line using the formula: m = (y2 - y1) / (x2 - x1). Substituting the given values, we get: m = (5 - 2) / (3 - 1) = 3/2.
Now, we can substitute the slope and one of the points into the point-slope form equation to get the final equation of the line. Let's use the point (1,2): y - 2 = (3/2)(x - 1).