Read the graph

Positive and negative slope: direction, steepness and signs

Separate a line’s direction from how sharply it changes.

The sign of a slope tells you the direction a line travels when read from left to right. Its absolute value tells you the magnitude of the change in y per unit of x. These are related but different ideas.

Positive slope rises to the right

For (0, 1) and (3, 7), the rise is 6 and the run is 3, so m = 2. Every unit increase in x corresponds to a 2-unit increase in y. Both coordinates do not have to be positive: (-4, -5) and (-1, 1) also give slope 2.

Negative slope falls to the right

For (0, 5) and (2, 1), the rise is -4 and the run is 2, so m = -2. As x increases, y decreases. A negative slope describes the relationship between changes, not the signs of the point coordinates.

Compare absolute values for steepness

On axes with the same units and scales, a line with slope -4 is steeper than a line with slope 2 because |-4| = 4 exceeds |2| = 2. The line falls rather than rises, but it changes more sharply. Slopes 2 and -2 have the same steepness in opposite directions.

If two graphs use different axis scales, their visual angles are not directly comparable. Always read the coordinates or numerical slopes rather than judging screenshots alone.

Moving in the opposite direction

On a negative-slope line, moving left makes y rise. Both changes reverse signs, leaving the quotient negative. This explains why swapping the order of the two points does not change the slope, provided both subtractions use the same order.

What the sign means in a context

If x is time and y is the amount of water in a tank, a negative slope could represent draining at a constant rate. The units are then water volume per time. A slope does not by itself prove causation, and a straight-line model may only apply over a limited interval.

Try positive and negative points in the calculator. To move from interpretation to equations, visit point-slope form. To review the numerator and denominator, see rise over run.