The coordinates of the y-intercept for the equation $y = x - 4$ are given by the point $(0, -4)$.

In a linear equation represented by the form $y = mx + c$, the y-intercept is the specific point where the line intersects the y-axis. This intersection occurs when the value of $x$ is equal to $0$. To determine the y-intercept, we substitute $x = 0$ into the equation and solve for $y$.

For the equation $y = x - 4$, we perform the substitution as follows:

Thus, when $x = 0$, we find that $y = -4$. This means that the line intersects the y-axis at the point $(0, -4)$. The y-intercept is an important point as it provides a reference for graphing the line and understanding its overall behavior.

In this scenario, the y-intercept indicates that the line begins 4 units below the origin on the y-axis. This information, along with the slope of the line (which is $1$ in this equation, corresponding to a 45-degree angle ascending to the right), is essential for accurately sketching the graph. It’s important to note that the y-intercept is always expressed as a coordinate pair, where the x-coordinate is $0$ and the y-coordinate represents the constant term from the equation.