The gradient of the line defined by the equation $y = x - 5$ is $1$.

To find the gradient of a line represented by the equation $y = mx + c$, one must identify the coefficient of $x$, which is denoted as $m$. In the equation $y = x - 5$, the coefficient of $x$ is $1$. This coefficient, $m$, signifies the gradient of the line. The gradient indicates the steepness and direction of the line’s slope. A positive gradient means the line rises as it moves from left to right, while a negative gradient indicates that it falls.

In the equation $y = x - 5$, since the coefficient of $x$ is $1$, the gradient is also $1$. This implies that for each unit increase in $x$, the value of $y$ increases by $1$ unit. The term $-5$ in the equation represents the y-intercept, which is the point at which the line intersects the y-axis. However, it is important to note that the y-intercept does not influence the gradient.

Understanding the gradient is essential for analyzing the behavior of linear functions. It allows us to predict how changes in $x$ will impact $y$. For instance, if you were to graph the line $y = x - 5$, you would begin at the y-intercept point $(0, -5)$. Using the gradient, you can determine additional points on the line. From $(0, -5)$, moving one unit to the right (increasing $x$ by $1$) results in moving one unit up (increasing $y$ by $1$), leading to the point $(1, -4)$, and this pattern continues onward.