Algebraically
Our function is #y=4x#. Looking at the slope-intercept form of a function it is #y=mx+b#, where m is the slope and b is the y-intercept. We can conclude that for our function the slope is 4 and the y-intercept is 0. Rate of change is defined as the slope of a line so our rate of change is 4. But this has no meaning. We can find the slope of a linear function using the following #m=\frac{y_1-y_2}{x_1-x_2}#. From this we can tell that our slope is equivalent to the following #m=4/1#. So for every unit #x# moves by, #y# moves 4 units.
Calculus
The slope of a function at a point is the derivative of the function at the point. The derivative of our function is just #y`(x)=4#. Since our derivative is a constant, the function is linear and has a constant slope of 4 units in the #y# direction for every unit #x# moves.
