Consider the following for the two (02) items that follow: The...

Given that the slope of the tangent to the curve $y = f(x)$ is $4$ for all $x$.

$\dfrac{dy}{dx} = 4$

Integrating both sides with respect to $x$:

$y = 4x + C$

Since the curve passes through the origin $(0, 0)$, substituting $x = 0$ and $y = 0$ gives:

$0 = 4(0) + C \Rightarrow C = 0$

The equation of the curve is $y = 4x$.

This represents a straight line. Checking the given points, for $x = 1$, $y = 4(1) = 4$.

Thus, the straight line passes through the point $(1, 4)$.