The y-intercept of the line given by the equation $y = 3x - 4$ is $-4$.

To elaborate, the y-intercept of a line is the point at which the line intersects the y-axis. This intersection occurs when the value of $x$ is $0$. To find the y-intercept, we substitute $x = 0$ into the line’s equation. For the equation $y = 3x - 4$, substituting $x = 0$ yields:

Thus, the y-intercept is $-4$.

In graphical terms, the y-intercept corresponds to the point $(0, -4)$. This means that if you were to plot the line represented by the equation $y = 3x - 4$ on a graph, it would cross the y-axis at the point where $y$ equals $-4$. This point is essential for accurately sketching the line.

Understanding the y-intercept is crucial as it provides a reference point for drawing the line. From this y-intercept, you can apply the slope (which in this case is $3$) to determine the line’s direction and steepness. The slope indicates that for every increase of $1$ unit in $x$, $y$ increases by $3$ units. By combining this information about the slope with the identified y-intercept, you can accurately plot the line on a graph.