To plot the function $y = |x - 3|$, you will create a V-shaped graph with its vertex located at the point $(3, 0)$.

First, it’s important to recognize that the absolute value function inherently produces a V-shape. The expression contained within the absolute value, $x - 3$, results in a horizontal shift of the graph. Specifically, this shift moves the vertex of the V from the origin $(0, 0)$ to the point $(3, 0)$. This occurs because the absolute value of zero is zero, and the equation $x - 3 = 0$ is satisfied when $x = 3$.

Next, let’s examine the behavior of the function on either side of the vertex. For values of $x \geq 3$, the absolute value function $|x - 3|$ simplifies to $x - 3$. Consequently, for $x$ values greater than or equal to 3, the graph is represented by a straight line with a slope of 1, extending upward to the right from the vertex $(3, 0)$.

Conversely, for values of $x < 3$, the absolute value function $|x - 3|$ simplifies to $-(x - 3)$, which is equivalent to $3 - x$. Therefore, for $x$ values less than 3, the graph forms a straight line with a slope of -1, rising upward to the left from the vertex $(3, 0)$.

In summary, begin by plotting the vertex at the point $(3, 0)$. Then, draw a line with a positive slope of 1 to the right of the vertex and a line with a negative slope of -1 to the left of the vertex. This construction will yield the distinctive V-shape characteristic of the absolute value function.