Given Information:
- Point (2, 3) lies on the line.
- The line intercepts the y-axis at a length of 3 units.
- The line intersects the equations y - 2x = 2 and y - 2x = 5.

Step 1: Find the slope of the line
Since the line intercepts the y-axis at a length of 3 units, we know that the y-intercept is (0, 3). Therefore, the slope of the line is given by:
slope = (change in y) / (change in x) = (3 - 0) / (2 - 0) = 3/2

Step 2: Find the equation of the line
Using the point-slope form of a line, which is y - y1 = m(x - x1), we can substitute the values of the point (2, 3) and the slope (3/2) into the equation:
y - 3 = (3/2)(x - 2)

Step 3: Simplify the equation
Distributing the slope term, we get:
y - 3 = (3/2)x - 3

Simplifying further, we have:
y = (3/2)x - 3 + 3
y = (3/2)x

Therefore, the equation of the line passing through the point (2, 3) and making an intercept of length 3 units is y = (3/2)x.

Explanation:
To find the equation of the line passing through the given point and intercepting the y-axis at a length of 3 units, we first need to determine the slope of the line. The slope is calculated by finding the change in y divided by the change in x between the y-intercept (0, 3) and the given point (2, 3).

Once we have the slope, we can use the point-slope form of a line to find the equation. The point-slope form is y - y1 = m(x - x1), where (x1, y1) represents the coordinates of a point on the line, and m represents the slope.

By substituting the values of the given point and slope into the point-slope form, we can simplify the equation to obtain the final equation of the line. In this case, the equation simplifies to y = (3/2)x.

Therefore, the equation of the line passing through the point (2, 3) and intercepting the y-axis at a length of 3 units is y = (3/2)x.