How is the slope of a line determined?

• A. By dividing the change in x by the change in y.
• B. By finding the length of the line segment.
• C. By multiplying the rise by the run.
• D. By dividing the rise (change in y) by the run (change in x).

Answer: (D)

The slope of a line is determined by the ratio of the vertical change to the horizontal change between two points on the line. This vertical change is referred to as the "rise," which represents how much the y-coordinate changes, while the horizontal change is known as the "run," indicating how much the x-coordinate changes.

To calculate the slope mathematically, you take the rise (the difference in the y-values of two points) and divide it by the run (the difference in the x-values of the same two points). This relationship is expressed as:

[

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

]

This method provides a consistent way to determine the steepness and direction of the line. If the slope is positive, the line rises as it moves from left to right, and if it is negative, the line falls. A slope of zero indicates a horizontal line, while an undefined slope indicates a vertical line.

Other options do not accurately describe how to find the slope. For example, dividing the change in x by the change in y incorrectly reverses the definition of slope. Finding the length of the line segment does not pertain to slope but rather measures distance. Multiplying