Question

Write the equation of a line that passes through (1, -1) and is perpendicular to the line (Y = frac{1}{2}X - 3).

a) (Y = -2X - 3)
b) (Y = 2X - 3)
c) (Y = -2X + 3)
d) (Y = 2X + 3)

Answer 1

The equation of the line that passes through (1, -1) and is perpendicular to Y = 1/2X - 3 is Y = -2X - 3.

Step-by-step explanation:

To find the equation of a line perpendicular to another line, we need to determine the negative reciprocal of the slope of the given line. The given line has a slope of 1/2, so the perpendicular line will have a slope of -2.

Using the point-slope form of the equation of a line, y - y1 = m(x - x1), we can substitute the coordinates of the given point (1, -1) and the slope (-2) into the equation. This gives us:

Y - (-1) = -2(X - 1).

Simplifying the equation, we get:

Y = -2X - 3.