The equation of line ab is y=-1/2x-1. write an equation of a line perpendicular to line ab in slope intercept form that contains point (-2,3). hint (y-y1=m(x-x1)

A perpendicular line has a slope that is the reciprocal of the original line.

y = -1/2x - 1

The slope is -1/2. The reciprocal of -1/2 is positive 2. You just flip the fraction, and change it from negative to positive (or the reverse).

Now, using y = mx + b, enter your new slope.

y = 2x + b

To find "b" now, just enter the coordinates you were given.

3 = 2(-2) + b
3 = -4 +b
7 = b

Enter the new "b" value into your equation for the answer.

The answer is: y = 2x + 7

The slope of the line given by y = -1/2x - 1 is -1/2
The slope of a line perpendicular to it is = -1 / (-1/2)  = 2
Substituting the point  (-2, 3) into  the point-slope form as given in the question, we have:-

y - 3 = 2(x - -2)
y = 2x + 4 + 3
y = 2x + 7 is the answer