Final answer:
The equation of the line that passes through (-5, -1) and is perpendicular to y = -2 is x = -5. This line is vertical, meaning it has an undefined slope and does not fit the typical y = mx + b slope-intercept form.
Step-by-step explanation:
To write the equation of a line that passes through the point (-5, -1) and is perpendicular to the line y = -2, we first need to determine the slope of the perpendicular line. Since the line y = -2 is horizontal, its slope is 0. Perpendicular lines have slopes that are negative reciprocals of each other. Therefore, the slope of the line we are looking for is undefined because the line is vertical.
A vertical line passing through (-5, -1) would have an equation of x = -5. This is because a vertical line has all points with the same x-coordinate. So, our equation in slope-intercept form is simply x = -5, which does not have a y-intercept or a slope in the traditional sense since it is not a function.