We have two points (-5, 7) and (-1, -5).
The equation of the line can be determined using the following equation:
y - y1 = [(y2 - y1)/(x2 - x1)]*(x -x1) [1]
Therefore:
x1 = -5
x2 = -1
y1 = 7
y2 = -5
Then, according to the equation [1]
y - 7 = [(-5 - 7)/(-1 -(-5))]*(x -(-5))
y - 7 = [(-12)/(-1+5)]*(x + 5)
y - 7 = [(-12)/4]*(x + 5)
y - 7 = (-12/4)*(x + 5)
y - 7 = -3 *(x + 5)
y - 7 = -3x - 15
y = -3x -15 + 7
y = -3x - 8
The equation of the line is then:
y = -3x - 8