The equation y=0.25x+10 is in slope-intercept form, y=mx+b where m is the slope and b is the y-intercept. The slope is the rate of change. The number in our equation that is in place of m is 0.25. This means for every change in x, the graph will go up 0.25. The rate of change is the same throughout the entire function, so this is a constant rate of change.
Since the rate of change is constant, the graph will be a straight line. A constant rate of change means there is the same distance between every two points on the graph; this is only true of a straight line.
Since the graph is a straight line, the function is linear by definition.
