m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.
The y-intercept is given by (0,a) = (0,-a). From this, we have that for it to be a function, a = -a, and the only value that respects this condition is a = 0, hence the y-intercept of the linear function is y = 0.
