The function f ( x ) is defined as 19 more than 4 times a number

Choice A is correct. It’s given that the function $f\left(x\right)$ is defined as $19$ more than $4$ times a number $x$. This can be represented by the equation $f\left(x\right)=4x+19$. The x-intercept of the graph of $y=f\left(x\right)$ in the xy-plane is the point where the graph intersects the x-axis, or the point on the graph where the value of $f\left(x\right)$ is equal to $0$. Substituting $0$ for $f\left(x\right)$ in the equation $f\left(x\right)=4x+19$ yields $0=4x+19$. Subtracting $19$ from each side of this equation yields $-19=4x$. Dividing each side of this equation by $4$ yields $x=-\frac{19}{4}$. Therefore, when $f\left(x\right)=0$, the number is $-\frac{19}{4}$. 

Choice B is incorrect. This is the best interpretation of the y-intercept, not the x-intercept, of the graph of the function.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect. This is the best interpretation of the slope, not the x-intercept, of the graph of the function.