The gradient of a line that is perpendicular to the line represented by the equation $y = -2x + 5$ is $\frac{1}{2}$.

To understand this, we first need to determine the gradient of the given line. The equation $y = -2x + 5$ is expressed in the slope-intercept form $y = mx + c$, where $m$ denotes the gradient. In this case, the gradient $m$ is $-2$.

A fundamental property of perpendicular lines is that the product of their gradients equals $-1$. Therefore, if one line has a gradient of $m$, the gradient of a line that is perpendicular to it can be calculated as $-\frac{1}{m}$.

In our scenario, the gradient of the given line is $-2$. To find the gradient of the line that is perpendicular to it, we take the negative reciprocal of $-2$. The reciprocal of $-2$ is $-\frac{1}{2}$, and taking the negative of that gives us $\frac{1}{2}$. Thus, the gradient of the line that is perpendicular to $y = -2x + 5$ is indeed $\frac{1}{2}$.

This implies that if you were to draw a line with a gradient of $\frac{1}{2}$, it would intersect the original line at a right angle. This concept is essential in geometry and has various applications, such as determining the shortest distance between a point and a line or constructing perpendicular bisectors in coordinate geometry.