Final answer:
To find the equation of a perpendicular line to y = -2x - 7 that passes through the point (-2, -3), we determine the slope to be the negative reciprocal which is 1/2. Using the slope-intercept form, the equation is y = 0.5x - 2, which is not listed in the student's options.
Step-by-step explanation:
To determine the equation representing the new path built perpendicular to the existing path given by the equation y = -2x - 7, we need to identify the slope of the new path. Since two lines that are perpendicular to each other have slopes that are negative reciprocals of each other, the slope of the new path will be the negative reciprocal of -2, which is 1/2. Given that the new path also passes through the point (-2, -3), we can use this point to find the y-intercept.
To find the y-intercept, we use the slope-intercept form of a line, which is y = mx + b, where m is the slope and b is the y-intercept. Substituting the known point (-2, -3) and the slope 1/2 into the equation, we get:
-3 = (1/2)(-2) + b
-3 = -1 + b
b = -2
Now that we have the y-intercept, the equation of the new path is y = 1/2x - 2, which simplifies to y = 0.5x - 2. This equation isn't listed in the choices provided by the student, so there may be an error in the choices or in understanding the question's premise. However, based on the explanations for constructing a perpendicular line given above, none of the choices given (A-D) correctly represents a perpendicular line to y = -2x - 7 passing through the point (-2, -3).