What is the formula for calculating the slope between two points?

What is the formula for calculating the slope between two points?

• A. (Y₁ - Y₂) / (X₂ - X₁)
• B. (Y₂ - Y₁) / (X₂ + X₁)
• C. (Y₂ - Y₁) / (X₂ - X₁)
• D. (Y₁ + Y₂) / (X₁ - X₂)

Answer: (C)

The formula for calculating the slope between two points is derived from the difference in the vertical coordinates (y-values) over the difference in the horizontal coordinates (x-values). In this case, the correct formula is represented as the change in y divided by the change in x, which is (Y₂ - Y₁) / (X₂ - X₁). This formula effectively measures how much y changes relative to how much x changes as you move from one point to the other. The numerator, (Y₂ - Y₁), reflects the vertical change (rise), while the denominator, (X₂ - X₁), represents the horizontal change (run). Thus, the slope provides the rate at which y changes for a given change in x, essential for understanding trends in mathematical functions, graphs, and even real-world scenarios. The other options either misuse the order of the coordinates or incorporate incorrect mathematical operations, which do not align with the standard definition of slope. Therefore, C is indeed the correct answer to calculate the slope between two points on a Cartesian plane.

The formula for calculating the slope between two points is derived from the difference in the vertical coordinates (y-values) over the difference in the horizontal coordinates (x-values). In this case, the correct formula is represented as the change in y divided by the change in x, which is (Y₂ - Y₁) / (X₂ - X₁).

This formula effectively measures how much y changes relative to how much x changes as you move from one point to the other. The numerator, (Y₂ - Y₁), reflects the vertical change (rise), while the denominator, (X₂ - X₁), represents the horizontal change (run). Thus, the slope provides the rate at which y changes for a given change in x, essential for understanding trends in mathematical functions, graphs, and even real-world scenarios.

The other options either misuse the order of the coordinates or incorporate incorrect mathematical operations, which do not align with the standard definition of slope. Therefore, C is indeed the correct answer to calculate the slope between two points on a Cartesian plane.