In short: A line has a positive gradient if it rises from left to right, and a negative gradient if it falls from left to right. Read the line in the direction of increasing x: up means positive, down means negative. A flat line has a gradient of zero.
Telling whether a gradient is positive or negative from a graph is a quick win on the GCSE Higher maths paper (AQA) — and a surprisingly common place to drop marks. You do not need to calculate anything to read the sign; you just need to read the line the right way. This guide shows you how to spot the sign at a glance, with a worked example and the traps to avoid.
The reliable method
To decide if a gradient is positive or negative from a graph, always read the line left to right (in the direction x increases).
- Find the left-hand end of the line. Put your eye or finger on the line at its leftmost point on the grid.
- Trace rightwards. Follow the line as x increases, moving towards the right of the grid.
- Decide up or down. If the line goes uphill as you move right, the gradient is positive. If it goes downhill, the gradient is negative.
- Spot the special cases. A perfectly horizontal line has gradient zero. A vertical line has an undefined gradient.
The whole trick is the direction you read in. Always left to right — never right to left, which reverses the apparent slope.
A worked example
A straight line on a graph passes through the points (0, 4) and (2, 0). Is its gradient positive or negative?
Step 1 — read left to right. The leftmost point is (0, 4), high up on the y-axis. As x increases towards (2, 0), the line drops down to the x-axis.
Step 2 — describe the direction. Moving right, the line goes downhill, from y = 4 down to y = 0. That is a falling line, so the gradient is negative.
Step 3 — confirm with the numbers (optional). Gradient = (0 − 4) ÷ (2 − 0) = (−4) ÷ 2 = −2. The minus sign confirms the line falls, exactly as the picture showed.
This works because gradient is the change in y for an increase in x. When y decreases as x increases, the change in y is negative, so the gradient is negative — and that is precisely what a downhill line looks like.
Common mistakes to avoid
- Reading right to left. Tracing the line backwards makes a falling line look like it rises. Always read in the direction of increasing x. Habitually overlooking the minus sign is the heart of [negative gradient sign blindness](/misconceptions/negative-gradient-sign-blindness).
- Judging by steepness, not direction. A steep line can be positive or negative. Steepness is the size of the gradient; the sign comes only from whether it rises or falls.
- Confusing the axes. Up–down is the y-direction; left–right is the x-direction. Mixing them up scrambles the reading.
- Assuming a line through the origin is positive. A line through (0, 0) can fall just as easily as it rises. Check its direction, not its starting point.
- Treating a near-flat line as zero. Only a truly horizontal line has gradient zero. A gently rising line still has a small positive gradient.
Frequently asked questions
How do you know if a line has a negative gradient? Read the line from left to right. If it falls — goes downhill as x increases — the gradient is negative. If it rises, the gradient is positive. You can confirm the sign by checking that y decreases as x increases.
What does a positive gradient look like on a graph? A positive gradient slopes uphill from left to right: as you move right, the line climbs. The larger the gradient, the steeper the climb.
Can you tell the sign of a gradient without calculating it? Yes. The direction of the line gives the sign immediately — uphill is positive, downhill is negative. You only need to calculate the value if the question asks for the actual number.
Does a steeper line always mean a bigger gradient? Steeper means a larger size of gradient, but the sign still depends on direction. A steep downhill line has a large negative gradient; a steep uphill line has a large positive gradient.
What is the gradient of a horizontal line on a graph? Zero. A horizontal line does not rise or fall, so y stays the same as x changes, giving a gradient of 0. A vertical line, by contrast, has an undefined gradient.
Practise this
See which slips cost you marks — [take the free diagnostic](/diagnostic). Related: [negative gradient sign blindness explained](/misconceptions/negative-gradient-sign-blindness).