Final answer:
The equation of the base of the isosceles triangle ABC, where y=-2, is y = (1/2)x + 1.
Step-by-step explanation:
The equation of the base of an isosceles triangle ABC, with y=-2, can be found by using the equation of one of its sides and the fact that the base is perpendicular to that side. The equation of the given side is y+2x=-1.
To find the slope of this line, we can rearrange the equation and write it in the form y=mx+b: y=-2x-1. Therefore, the slope of the given side is -2.
Since the base is perpendicular to the given side, its slope will be the negative reciprocal of -2. The negative reciprocal of -2 is 1/2. Using the point-slope form of a line, y-y1=m(x-x1), where (x1, y1) is a point on the line and m is the slope, we can substitute y1=-2, m=1/2, and x1=-1 into the equation.
This gives us the equation of the base as y + 2 = (1/2)(x + 1). Rearranging this equation, we get y = (1/2)x + 1.