Which expression correctly represents the slope formula?

Which expression correctly represents the slope formula?

• A. m = (y2 - y1) / (x2 - x1)
• B. m = (y1 - y2) / (x2 - x1)
• C. m = (x2 - x1) / (y2 - y1)
• D. m = (y2 - y1) / (x1 - x2)

Answer: (A)

Slope is rise over run: it compares how much y changes when x changes, between two points on the line. If you take two points (x1, y1) and (x2, y2), the slope is (y2 − y1) divided by (x2 − x1). This keeps the direction from the first point to the second point consistent, so you get the true rate of change. The other forms mix up the idea. Using (y1 − y2) instead of (y2 − y1) flips the sign, giving the negative slope. Swapping the x-difference to (x1 − x2) also flips the sign for the same reason. Putting the x-difference in the numerator and the y-difference in the denominator yields the reciprocal of the slope, which describes a different relationship.

Slope is rise over run: it compares how much y changes when x changes, between two points on the line. If you take two points (x1, y1) and (x2, y2), the slope is (y2 − y1) divided by (x2 − x1). This keeps the direction from the first point to the second point consistent, so you get the true rate of change.

The other forms mix up the idea. Using (y1 − y2) instead of (y2 − y1) flips the sign, giving the negative slope. Swapping the x-difference to (x1 − x2) also flips the sign for the same reason. Putting the x-difference in the numerator and the y-difference in the denominator yields the reciprocal of the slope, which describes a different relationship.