To solve this problem, we first need to find the slope of the given line, y = 2x + 3. In the slope-intercept form of a linear equation, y = mx + b, 'm' represents the slope of the line. So, the slope of the given line is 2.
Next, we need to find the slope of the line that is perpendicular to the given line. We can determine this by taking the negative reciprocal of the slope of the given line. The negative reciprocal of 2 is -1/2, which is the slope of the line that is perpendicular to the given line.
Now that we have the slope of the line we want to find, we move on to find the equation of the line. We can use the point-slope formula, y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. Here, the point given is (2,3). Substituting these values in, we get, y - 3 = -1/2 * (x - 2).
Solving the above equation gives us the equation of the line as y = -1/2*x + 3 + 1. Simplifying further, we get the equation of the line that is perpendicular to the given line and passes through the point (2,3) as y = -1/2*x + 4.