What is an equation of the line that passes through the points (-6, 5) and (6, -7)

Equation of a line is y=mx+c
m is the gradient and c is the y intercept

gradient = change in y / change in x
so it would be -7-5 divided by 6 - -6 = -12/12 = -1

the equation is now y = -x+c

now to find the y intercept you substitute one of the given coordinates into the equation we already have
(6,-7) —> -7= -(-7) + c
= -7 = 7 + c
= c = -14

we put that back into the equation to get line
y = -x - 14