What is the formula for calculating the slope between two points (X1, Y1) and (X2, Y2)?

What is the formula for calculating the slope between two points (X1, Y1) and (X2, Y2)?

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

Answer: (A)

The correct formula for calculating the slope between two points, (X1, Y1) and (X2, Y2), is derived from the concept of rise over run. The slope represents the change in the y-values divided by the change in the x-values. To find the slope, you first determine the change in the y-coordinate, which is calculated as (Y2 - Y1), and the change in the x-coordinate, which is (X2 - X1). Therefore, the slope (m) can be expressed as: m = (Y2 - Y1) / (X2 - X1). This indicates how much y changes for each unit change in x. However, in one of the answer choices given, the expression is rearranged to focus on (Y2 - Y1) as the numerator and (X1 - X2) as the denominator. If we multiply both the numerator and denominator by -1, we can indeed express this as: m = (Y1 - Y2) / (X1 - X2). This is mathematically valid because multiplying by -1 simply changes the sign of both the rise and run, but the slope remains the same. Thus, the choice that states (

The correct formula for calculating the slope between two points, (X1, Y1) and (X2, Y2), is derived from the concept of rise over run. The slope represents the change in the y-values divided by the change in the x-values.

To find the slope, you first determine the change in the y-coordinate, which is calculated as (Y2 - Y1), and the change in the x-coordinate, which is (X2 - X1). Therefore, the slope (m) can be expressed as:

m = (Y2 - Y1) / (X2 - X1).

This indicates how much y changes for each unit change in x.

However, in one of the answer choices given, the expression is rearranged to focus on (Y2 - Y1) as the numerator and (X1 - X2) as the denominator. If we multiply both the numerator and denominator by -1, we can indeed express this as:

m = (Y1 - Y2) / (X1 - X2).

This is mathematically valid because multiplying by -1 simply changes the sign of both the rise and run, but the slope remains the same.

Thus, the choice that states (