The coordinates of the y-intercept in the equation $y = -2x + 7$ are given by the point $(0, 7)$.

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

For the equation $y = -2x + 7$, substituting $x = 0$ yields:

Consequently, the y-intercept is the point where $x = 0$ and $y = 7$, which can be expressed as the coordinates $(0, 7)$.

Understanding the y-intercept is vital, as it serves as a foundational point for graphing the line. It indicates the location where the line crosses the y-axis, facilitating accurate plotting of the graph. In this instance, the line intersects the y-axis at the point $(0, 7)$. This implies that regardless of the value of $x$, when $x = 0$, the value of $y$ will consistently be $7$.

Furthermore, the slope of the line, represented by $m$ in the equation $y = mx + c$, indicates the steepness of the line. In this scenario, $m = -2$, signifying that the line descends from left to right. By combining this information about the slope with the y-intercept, you can accurately sketch the line on a graph.