A line through (1, 2) and (3, 4) has what slope?

To find the slope of the line that passes through the points (1, 2) and (3, 4), you can use the slope formula, which is given by

[

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

]

In this case, let's designate (x₁, y₁) as (1, 2) and (x₂, y₂) as (3, 4). Plugging these coordinates into the formula, we get:

[

\text{slope} = \frac{4 - 2}{3 - 1} = \frac{2}{2} = 1

]

Thus, the slope of the line is 1. This means that for every increase of 1 unit in the x-direction, the line rises by 1 unit in the y-direction, indicating a consistent, positive linear relationship between the two points.

Understanding the options in this context helps clarify that a slope of 0 would indicate a horizontal line, a slope of 2 would mean a steeper incline than what we calculated, and a slope of 3 would indicate an even steeper incline beyond what