Which expression correctly represents the slope formula?

Which expression correctly represents the slope formula?

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

Answer: (B)

Slope measures how steep a line is by comparing how much you rise or fall to how much you move left or right. This rate of vertical change with respect to horizontal change is written as the difference in y-values over the difference in x-values: (y2 − y1) / (x2 − x1). This form directly captures how much the line climbs for each unit moved to the right, which is exactly what slope represents. Using (x2 − x1) / (y2 − y1) would give the reciprocal of the slope, not the slope itself. Using just Y2 − Y1 or just X2 − X1 omits the necessary division, so they describe only vertical change or only horizontal change, not the rate of change along the line. For example, between points (1, 2) and (3, 6), the slope is (6 − 2) / (3 − 1) = 4 / 2 = 2, meaning the line rises 2 units for every 1 unit it moves to the right.

Slope measures how steep a line is by comparing how much you rise or fall to how much you move left or right. This rate of vertical change with respect to horizontal change is written as the difference in y-values over the difference in x-values: (y2 − y1) / (x2 − x1). This form directly captures how much the line climbs for each unit moved to the right, which is exactly what slope represents.

Using (x2 − x1) / (y2 − y1) would give the reciprocal of the slope, not the slope itself. Using just Y2 − Y1 or just X2 − X1 omits the necessary division, so they describe only vertical change or only horizontal change, not the rate of change along the line.

For example, between points (1, 2) and (3, 6), the slope is (6 − 2) / (3 − 1) = 4 / 2 = 2, meaning the line rises 2 units for every 1 unit it moves to the right.