#50
Top 50 Mistake
Calculating gradient with x over y instead of y over x
"The Gradient Flip"
The Mistake in Action
Find the gradient of the line through (1, 2) and (4, 8).
Wrong: $m = \frac{4 - 1}{8 - 2} = \frac{3}{6} = 0.5$
Why It Happens
Students mix up which values go on top and bottom. They may remember "rise over run" but forget which is which.
The Fix
Gradient = change in y over change in x
$$m = \frac{y_2 - y_1}{x_2 - x_1}$$
Memory aids:
- "y over x" — alphabetically, y comes after x, so y is on top
- "Rise over run" — rise (vertical/y) comes before run (horizontal/x)
$$m = \frac{8 - 2}{4 - 1} = \frac{6}{3} = 2$$
Spot the Mistake
Can you identify where this student went wrong?
Find the gradient through (1, 2) and (4, 8)
$m = \frac{4-1}{8-2} = \frac{3}{6}$
$= 0.5$
Click on the line that contains the error.
Related Topics
Learn more about the underlying maths: