Final answer:
The equation of the line perpendicular to Y = 1/2X -3 and passing through the point (1,-1) is y = -2x + 1. This is found by determining the perpendicular slope to be -2 and using the point-slope form to get the equation.
Step-by-step explanation:
To find an equation of a line that is perpendicular to the line Y = 1/2X -3, we need to determine the perpendicular slope. The slope of the given line is 1/2, and the slope of a line perpendicular to it will be the negative reciprocal, which in this case is -2. The line must also pass through the point (1,-1).
Using the point-slope form of a line equation, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line, we can substitute the slope m = -2 and the point (1, -1) to find the equation of our perpendicular line:
y - (-1) = -2(x - 1)
y + 1 = -2x + 2
y = -2x + 1
Thus, the equation of the line that is perpendicular to Y = 1/2X -3 and passes through the point (1,-1) is y = -2x + 1.