Quick answer
Slope measures how much y changes when x changes. For a straight line, it is the same between any two points.
Use rise over run
Slope = change in y ÷ change in x. From (1, 2) to (4, 8), the rise is 6 and the run is 3, so slope = 2.
Use the two-point formula
m = (y2 - y1)/(x2 - x1), provided x2 is not equal to x1.
Interpret the sign
Positive slope rises left to right. Negative slope falls. A horizontal line has slope zero; a vertical line has undefined slope.
Worked examples
(1, 2) to (4, 8) → m = 2(0, 5) to (2, 1) → m = -2(1, 3) to (4, 3) → m = 0
Common mistake to avoid
Subtract coordinates in the same order on top and bottom; mixing orders changes the sign.
Practice questions
Try these without looking at the answers first. Explain your reasoning aloud or write each step.
- Question:
(0, 0) to (2, 6)— Answer:3 - Question:
(1, 4) to (3, 0)— Answer:-2 - Question:
(2, 5) to (5, 5)— Answer:0
What to learn next
Review the related lessons linked below, then practice independently. If you make an error, write down which rule you used and why it did not apply.