gradient

of: a straight line (or the corresponding linear function)

is: a measure of the rate at which one quantity changes with another quantity. As a graph with given scales on the Cartesian axes, the gradient controls the angle between the line and the horizontal.

is often used synonymously with: the slope of the straight line.

is given: for a straight line drawn as a graph on conventional Cartesian axes, with horizontal and vertical, by the ratio of a difference in values to the corresponding difference in values between any two points on the straight line,

i.e. [M1.3, M2.2, P1.3]

may be easily found: from the gradient-intercept form of the equation of a straight line, where it is represented by the constant

may be used more generally: at a point on a curve, to refer to the gradient of the straight line that is a tangent to the curve at the point.

is equal, in this more general sense; to the derivative of the function that describes the curve, evaluated at the point in question

i.e. the gradient of at is [M4.2]