The gradient of the line that passes through the points $(1, 4)$ and $(3, 10)$ is equal to $3$.

To determine the gradient of a line, we utilize the formula:

This formula allows us to assess the steepness of the line by comparing the vertical change (often referred to as “rise”) to the horizontal change (known as “run”) between two points on the line.

Let’s apply this formula to the specified points $(1, 4)$ and $(3, 10)$. We start by identifying the coordinates: the first point, denoted as $(x_1, y_1)$, is $(1, 4)$, and the second point, denoted as $(x_2, y_2)$, is $(3, 10)$.

Next, we calculate the change in $y$ (the vertical change) and the change in $x$ (the horizontal change):

Now, we substitute these values into the gradient formula:

Thus, the gradient of the line that passes through the points $(1, 4)$ and $(3, 10)$ is $3$. This indicates that for every unit you move horizontally to the right along the line, the line ascends vertically by $3$ units. Understanding the gradient is essential for analyzing the steepness and direction of a line in a graph.