Positive slope

A line has a positive slope when it rises as you move from left to right across the graph. Slope measures steepness as rise over run: m = (y₂ − y₁) / (x₂ − x₁). When that value is greater than zero, an increase in x always produces an increase in y — the two variables move in the same direction.

For example, the line through (1, 2) and (4, 8) has slope m = (8 − 2) / (4 − 1) = 2, a positive slope: every step right moves the line two steps up. In slope-intercept form y = mx + b, any positive m — steep like m = 5 or gentle like m = 0.1 — produces an upward-sloping line. Compare the alternatives: a negative slope falls left to right, a zero slope is horizontal, and a vertical line has an undefined slope.

Positive slope carries meaning in applied graphs. On a position-versus-time graph, a positive slope means an object is moving in the positive direction, since slope there equals velocity. In calculus, a positive derivative — the slope of the tangent line — tells you a function is increasing at that point. In statistics and economics, an upward-sloping line signals a direct (positive) relationship between two variables.

Slope questions appear across standardized tests: the GRE tests reading slope from equations and coordinate pairs, AP Physics 1 uses graph slopes to extract velocity and acceleration, and AP Calculus AB connects positive slope to positive derivatives and increasing functions.