y = mx + b, m is the slope, b is the y-intercept

lets find the slope m

m = (-2-5)/(6-(-5))

m = -7/11

y = -7x/11 + b

lets find b the y-intercept

the lines goes trough (-5,5) thus

5 = -7*(-5)/11 + b

b = 20/11

the equation of the line trough (-5,5) and (6,-2) is

y = -7x/11 + 20/11