Question

When a river​ flows, the strength or force of the river depends on how far the river falls vertically compared to how far it flows horizontally. Find the slope of the river shown to the right.​ (Hint: The slope of a river is​ positive.)

Answer 1

The figure is missing. There are several problems with same wording but different numbers

Here, we can use:

• Horizontal distance: 258 feet

• Vertical fall: 56.0 feet

Answer:

• Slope = 56.0 ft / 258 ft ≈ 0.217

Explanation:

The slope measures how the rate of change of the vertical distance (vertical fall) with respect to the horizontal distance.

There are several forms to express this with words, which represent the same formula. Here are some of them:

• Slope = rise / run
• Slope = vertical change / horizontal change
• Slope = change in y / change in x
• Slope = Δy / Δx
• Slope = (y₂ - y₁) / (x₂ - x₁)

As said, all those forms mean the same; they are equivalent.

Here, we have vertical fall = 56.0 feet, and horizontal distance = 258 feet, and by specifications of the problem (in the hint) the slope must be positive. Thus, you get:

• Slope = vertical fall / horizontal distance = 56.0 feet / 258 feet ≈ 0.217