The solution for this will be done in the following steps:
1) Understand the given line: The line equation y = 1/2x - 3 is in the slope-intercept form (y = mx + c), where m is the slope and c is the y-intercept. Here, the slope of the given line (m1) is 1/2. So m1 = 1/2.
2) Understanding the property of parallel lines: The slopes of two lines are equal if and only if the lines are parallel. Therefore, the slope of the line we need to find (m2) which is parallel to the given line will be equal to m1, so m2 = m1 = 1/2.
3) Coordinate values for the point: For the point through which the line passes, (x1, y1) - let’s assume that we don't know the exact point, so we'll denote it as (a, b)
4) Using the point-slope form of the line equation: The equation of a line in the point-slope form is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.
5) Substituting the values: Substituting m2 for m and (a, b) for (x1, y1), the equation of the line becomes y - b = 1/2 * (x - a).
So, the equation of the line parallel to the given line and passing through the point (a, b) is y - b = 1/2 * (x - a).
You can substitute (a, b) with any point you wish the line to pass through, then simplify to find the equation of the line.