What is the rise over run in a triangle with a rise of 4 and a run of 3?

The rise over run is a way to describe the slope of a line or the steepness of a triangle, particularly in the context of coordinate geometry. In this case, the rise is 4 and the run is 3. The slope is calculated by taking the rise (the vertical change) and dividing it by the run (the horizontal change).

So, the slope or rise over run is calculated as:

[

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

]

This result tells us that for every 3 units moved horizontally to the right, the line moves upward by 4 units. By expressing the rise over run as a fraction, it can clearly communicate the relationship between the vertical change and the horizontal change.

The fraction ( \frac{4}{3} ) represents the slope in its simplest form. This value is also equivalent to approximately 1.33 when expressed as a decimal, but the fraction directly represents the ratio of rise to run more clearly, especially in mathematical contexts where fractions are often preferred.

Understanding this concept is crucial for interpreting and solving problems involving slopes in various mathematical and real-world scenarios.