How is slope defined in mathematical terms?

The definition of slope in mathematical terms is represented as "rise/run." Slope measures the steepness or incline of a line on a graph and is calculated by dividing the change in the vertical direction (rise) by the change in the horizontal direction (run). This concept is fundamental in algebra and geometry, as it helps to understand the rate of change between two variables.

When analyzing a linear relationship, for every unit increase in the horizontal direction (the x-axis), the slope tells us how much the value on the vertical direction (the y-axis) changes. A positive slope indicates that as the x-values increase, the y-values also increase, which corresponds to an upward slant to the right. Conversely, a negative slope indicates a downward trend.

The other options do not correctly define slope. The y-intercept relates to the location where a line crosses the y-axis, but it does not inform about the angle or steepness of the line. Length times width does not relate to slope; it pertains to area. Lastly, the x-coordinate minus the y-coordinate does not provide meaningful information about the relationship between the two variables and does not reflect the concept of slope.