Final answer:
To find the equation of the line perpendicular to y=-2x-1 and passing through (2, -1), determine the negative reciprocal of the original line's slope, which is 1/2, and then apply the point-slope formula to get the equation y = 1/2x - 1.
Step-by-step explanation:
The equation of a line is typically written in the form y = mx + b, where m represents the slope of the line and b represents the y-intercept. If a line is perpendicular to another line, its slope is the negative reciprocal of the other line's slope. Since the slope of the given line y=-2x-1 is -2, the slope of the perpendicular line will be 1/2.
To find the equation of the line that is perpendicular to y=-2x-1 and passes through the point (2, -1), we use the point-slope form of the line equation, which is y - y1 = m(x - x1) where (x1, y1) is a point on the line. Substituting the known values, we get y - (-1) = 1/2(x - 2), which simplifies to y = 1/2x - 2 + 1 or y = 1/2x - 1 as the final equation of the line.