Assessment and Learning in Knowledge Spaces (ALEKS) Basic Math Placement Practice Test

If given two points, how do you calculate the slope between them?

1. (y1 + y2) / (x1 + x2)

2. (y2 - y1) / (x2 - x1)

3. (x2 - x1) / (y2 - y1)

4. (y1 - y2) / (x1 + x2)

The correct answer is: (y2 - y1) / (x2 - x1)

To calculate the slope between two points on a coordinate plane, you use the formula for slope, which is defined as the change in the vertical direction (y-coordinates) divided by the change in the horizontal direction (x-coordinates). This is mathematically expressed as (y2 - y1) / (x2 - x1). Using this formula, you find the difference in the y-values of the two points, which tells you how much the line rises or falls between those two points. Then, you divide this difference by the difference in the x-values, which indicates the horizontal distance over which this rise or fall occurs. The result gives you the slope of the line connecting the two points, demonstrating the steepness and direction of the line. This formula provides a straightforward way to understand the relationship between the coordinates of the two points and is foundational in algebra and understanding linear relationships.