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

y = (1/2)x + 1/2

Step-by-step 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

where is the figure