Any spot on a graph is defined by a coordinate with a value on the x axis (horizontal) and the y axis (vertical). An equation like the one you gave can be used to find each point on a given line. Therefore, this equation is the equation for a line (in slope intercept form).
y is the value of y for a coordiinate that is given in (x,y) form.
m is the slope of the line.
x is the value of x
n is the y-intercept. It is the value for y when x = 0 and therefore that is the point where the line crosses the y axis.
y=mx+n represents the equation of the line, written in the slope intercept form.
m represents the slope of the line. The slope is the value of tangent of the angle made by the line to x axis.
n represents the y intercept of the line.
The axis intercepting points are found in this way:
x = 0 => y intercepting => the point that belongs to the line, (0,y).
y = 0 => x intercepting => the point that belongs to the line, (x,0).