Answer:
y = (1/2)x + 1/2
Explanation:
An equation, y = -2x+2, is given; its slope is -2. We are to find the equation of a line which is perpendicular to this given line; the slope of the perpendicular has a slope which is the negative reciprocal of that of the given line. Thus, the slope of the perpendicular is
-1
m = -------------- = +1/2.
-2
This perpendicular is to pass through (-5,-2). Plugging these x- and y-coordinates and the slope m = 1/2 into the point-slope formula for a straight line, we get:
y-[-2] = (1/2)(x-[-5]), or y + 2 = (1/2)(x + 5).
This is the correct answer. If, however, you want this equation in slope-intercept form, do the following:
Mult. all three terms of y + 2 = (1/2)(x + 5 by 2 to eliminate the fraction 1/2:
2y + 4 = x + 5. Solve this for y: Subtract 4 from both sides, obtaining:
2y = x + 1. Finally, multiply all terms by 1/2: y = (1/2)x + 1/2