Final answer:
The equation of the line passing through the point (-5, -11) that is perpendicular to the line between (-2, 1) and (2, -1) is y = 2x - 1.
Step-by-step explanation:
To find the equation of the line that goes through the point (-5, -11) and is perpendicular to the line passing through (-2, 1) and (2, -1), we first need to determine the slope of the given line. The slope (m) of a line through points (x1, y1) and (x2, y2) can be calculated using the formula m = (y2 - y1) / (x2 - x1).
For the line through (-2, 1) and (2, -1), we calculate the slope:
m = (-1 - 1) / (2 + 2) = -2 / 4 = -1/2
The slope of a line perpendicular to this line will be the negative reciprocal of -1/2, which is 2.
Using the point-slope form of the equation y - y1 = m(x - x1) and the point (-5, -11), we plug in our values:
y - (-11) = 2(x - (-5))
Simplifying:
y + 11 = 2(x + 5)
y = 2x + 10 - 11
y = 2x - 1
The equation of the line that is perpendicular to the line passing through (-2, 1) and (2, -1) and goes through the point (-5, -11) is y = 2x - 1.