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Find the equation of a line passing through the given point and perpendicular to the given equation (-5,-2) and y=-2x+2

2 Answers

3 votes

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

User Andrzej Zabost
by
8.1k points
5 votes

Answer:

y=1/2x+ 1/2


Explanation:


User Makeeva
by
8.0k points

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