What is the slope of a line that passes through the points (2, 3) and (4, 7)?

To determine the slope of a line that passes through two points, we can use the formula for slope, which is given by:

[ \text{slope} (m) = \frac{y_2 - y_1}{x_2 - x_1} ]

In this case, we have two points: (2, 3) and (4, 7). Here, (x₁, y₁) = (2, 3) and (x₂, y₂) = (4, 7).

Substituting the values into the slope formula:

[ m = \frac{7 - 3}{4 - 2} ]

[ m = \frac{4}{2} ]

[ m = 2 ]

Thus, the slope of the line that passes through the points (2, 3) and (4, 7) is indeed 2. This indicates that for every unit increase in the x-direction, the y-value increases by 2 units. Such a positive slope reflects an upward trend as you move from left to right on the graph, confirming the relationship between the two points on the line.