Final answer:
The equation of the line perpendicular to 2x + y = -5, which passes through the point (-1,-2), is found by first determining the negative reciprocal of the slope of the original line and then using the point-slope form to get y = 1/2x - 1.
Step-by-step explanation:
To find the equation of a line perpendicular to the given line 2x + y = -5, we first need to determine the slope of the given line. In slope-intercept form, y = mx + b, the coefficient of x represents the slope. The given equation can be written in slope-intercept form by solving for y:
y = -2x - 5
The slope of this line is -2. Since perpendicular lines have slopes that are negative reciprocals of each other, the slope of the line perpendicular to the given line would be 1/2.
Now, to find the equation of the perpendicular line that passes through the point (-1, -2), we use the point-slope form of the equation:
y - y1 = m(x - x1), where (x1, y1) is the point and m is the slope. Substituting the point and slope in, we get:
y - (-2) = 1/2(x - (-1))
Simplifying the equation, we arrive at:
y + 2 = 1/2x + 1/2
Finally, subtracting 2 from both sides gives us:
y = 1/2x - 3/2
Converting the fraction to integer form, the equation becomes:
y = 1/2x - 1.
Hence, the answer is d) y = 1/2x - 1.