Answer:
y = -4x - 6
Step-by-step explanation:
The equation of a line in point-slope form.
[tex] y - y_1 = m(x - x_1) [/tex]
is the equation of the line containing point (x1, y1) and having slope, m.
The given point of the perpendicular bisector is (-1, -2), so in this case, x1 = -1, and y1 = -2.
We need the slope of the perpendicular bisector. First we find the slope of the segment. We start at point (-5, -3). We go up 1 unit and 4 units to the right, and we are at another point on the segment. Since slope = rise/run, the slope of the segment is 1/4. The slopes of perpendicular lines are negative reciprocals, so the slope of the perpendicular bisector is the negative reciprocal of 1/4, so for the perpendicular bisector, m = -4.
Now we use the equation above and our values.
[tex] y - y_1 = m(x - x_1) [/tex]
[tex] y - (-2) = -4(x - (-1)) [/tex]
[tex] y + 2 = -4(x + 1) [/tex]
[tex] y + 2 = -4x - 4 [/tex]
[tex] y = -4x - 6 [/tex]
