Final answer:
To find the equation of a line parallel to y - 3 = -3/2x that passes through the point (4, -5), we need to find the slope of the given line and substitute the coordinates of the given point into the equation of the parallel line.
Step-by-step explanation:
To find the equation of a line parallel to y - 3 = -3/2x that passes through the point (4, -5), we need to determine the slope of the given line and use it to construct the equation of the parallel line. The given line can be rewritten as y = -3/2x + 3, where the slope is -3/2. Since the parallel line has the same slope, the equation will be y = -3/2x + b. We can substitute the coordinates of the given point (4, -5) to find the y-intercept (b).
Substituting the values, we get -5 = -3/2 * 4 + b. Simplifying this gives us -5 = -6 + b. Adding 6 to both sides of the equation, we find b = 1. Therefore, the equation of the line parallel to y - 3 = -3/2x that passes through the point (4, -5) is y = -3/2x + 1.