The gradient of the linear equation $y = -5x + 3$ is equal to -5.

To grasp how to determine the gradient of a linear equation, we can analyze the expression $y = -5x + 3$. This equation is structured in the standard form $y = mx + c$, where $m$ denotes the gradient (or slope) and $c$ indicates the y-intercept. The gradient $m$ provides insight into the steepness and direction of the line.

In the equation $y = -5x + 3$, the coefficient of $x$ is -5, which represents the gradient. Therefore, we conclude that the gradient of the line is -5. This implies that for every unit increase of 1 in $x$, the value of $y$ decreases by 5 units. The negative sign signifies that the line descends from left to right.

To visualize this concept, consider plotting the line on a graph. Begin at the y-intercept, which is the point where the line intersects the y-axis. In this case, the y-intercept is 3, corresponding to the constant term in the equation. From this point, if you move 1 unit to the right along the x-axis, you would move 5 units downward along the y-axis due to the gradient being -5. This downward movement illustrates the negative slope of the line.

Understanding the gradient is essential for analyzing the behavior of linear functions and predicting how variations in $x$ influence $y$.