# Question 5d05a

$y$ increases 4 units for every 1 unit $x$ increases.
Our function is $y = 4 x$. Looking at the slope-intercept form of a function it is $y = m x + b$, 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 $m = \setminus \frac{{y}_{1} - {y}_{2}}{{x}_{1} - {x}_{2}}$. From this we can tell that our slope is equivalent to the following $m = \frac{4}{1}$. So for every unit $x$ moves by, $y$ moves 4 units.
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.