What is the slope of a line that rises 3 units for every 4 units it runs?

The slope of a line is defined as the "rise" over the "run." In this case, the problem states that the line rises 3 units for every 4 units it runs. This means that for every 4 units you move horizontally to the right, the line ascends 3 units vertically.

To find the slope, we take the rise (which is 3) and divide it by the run (which is 4). Therefore, the slope is calculated as:

[

\text{slope} = \frac{\text{rise}}{\text{run}} = \frac{3}{4}

]

This fraction, 3/4, represents the rate of change of the line and indicates that for every 4 units moved along the x-axis (horizontal direction), the line increases by 3 units in the y-axis (vertical direction).

Understanding the concept of slope is important for graphing lines and understanding linear relationships in mathematics. The correct choice reflects the proper calculation and understanding of how slope is derived from rise and run.