Step 1 :The equation of a line in slope-intercept form is given by \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.
Step 2 :We are given that the slope \(m = 1\) and the line passes through the point \((-7,-8)\).
Step 3 :We can substitute these values into the equation to find the y-intercept \(b\).
Step 4 :Given that \(m = 1\) and \(b = -1\), the final equation of the line is \(y = x - 1\).
Step 5 :\(\boxed{y = x - 1}\)