Find the slope of the line that passes through the points (2, 3) and (4, 7).

To find the slope of the line that passes through the given points (2, 3) and (4, 7), the formula used is:

[

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

]

In this case, the points can be identified as:

• ( (x_1, y_1) = (2, 3) )

• ( (x_2, y_2) = (4, 7) )

Substituting these values into the slope formula gives:

[

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

]

Thus, the slope of the line connecting these two points is 2. The slope represents how steep the line is. A slope of 2 indicates that for every increase of 1 unit in the x-direction, the y-value increases by 2 units, reflecting a positive linear relationship between the points.

This calculation confirms that the correct answer is indeed 2. Understanding how to determine the slope using these points is crucial for analyzing linear relationships in the coordinate plane.