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

To determine the slope of the line that passes through the points (2, 3) and (4, 7), you can use the formula for calculating the slope between two points, which is given by:

[

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

]

In this case, you can assign the coordinates as follows: ( (x_1, y_1) = (2, 3) ) and ( (x_2, y_2) = (4, 7) ). Plugging these values into the formula, you would calculate:

[

\text{slope} = \frac{7 - 3}{4 - 2} = \frac{4}{2} = 2

]

This shows that the slope of the line is indeed 2, indicating that for every unit increase in x, the value of y increases by 2 units. This reflects a steep, upward inclination of the line.

Understanding the slope is crucial in various contexts, such as analyzing trends or predicting outcomes in linear equations, making the correct identification of the slope highly valuable in both theoretical and applied mathematics.