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 points (2, 3) and (4, 7), you use the formula for slope, which is defined as the change in the y-coordinates divided by the change in the x-coordinates. This can be expressed mathematically as:

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

]

Here, you can designate the first point (2, 3) as ((x_1, y_1)) and the second point (4, 7) as ((x_2, y_2)). Substituting the coordinates into the slope formula gives:

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

Thus, the slope of the line that connects these two points is 2. Understanding the slope in this context helps visualize the line's steepness; a slope of 2 indicates that for every 2 units the line rises, it moves 1 unit across the horizontal axis. This positive slope confirms an upward trend from left to