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Slope illustrated for y = (3/2)x − 1.Click on to enlarge Slope of a line in coordinates system, from f(x) = −12x + 2 to f(x) = 12x + 2. The slope of a line in the plane containing the x and y axes is generally represented by the letter m, [5] and is defined as the change in the y coordinate divided by the corresponding change in the x coordinate, between two distinct points on the line.
a is frequently referred to as the slope of the line, and b as the intercept. If a > 0 then the gradient is positive and the graph slopes upwards. If a < 0 then the gradient is negative and the graph slopes downwards. For a function (, …,) of any finite number of variables, the general formula is
If it is positive then the graph has an upward concavity, and, if it is negative the graph has a downward concavity. If it is zero, then one has an inflection point or an undulation point . When the slope of the graph (that is the derivative of the function) is small, the signed curvature is well approximated by the second derivative.
If the slope is positive, >, then the function () is increasing; if <, then () is decreasing In calculus , the derivative of a general function measures its rate of change. A linear function f ( x ) = a x + b {\displaystyle f(x)=ax+b} has a constant rate of change equal to its slope a , so its derivative is the constant function f ′ ( x ) = a ...
The figure at right illustrates the formula. Notice that the slope in the example of the figure is negative. The formula also provides a negative slope, as can be seen from the following property of the logarithm: (/) = (/).
A simple two-point estimation is to compute the slope of a nearby secant line through the points (x, f(x)) and (x + h, f(x + h)). [1] Choosing a small number h, h represents a small change in x, and it can be either positive or negative. The slope of this line is (+) ().
Notice that the points (2,1) and (2,3) are on opposite sides of the line and (,) evaluates to positive or negative. A line splits a plane into halves and the half-plane that has a negative (,) can be called the negative half-plane, and the other half can be called the positive half-plane. This observation is very important in the remainder of ...
It can be expressed by numerous definitions, for example "0 for negative inputs, output equals input for non-negative inputs". The term "ramp" can also be used for other functions obtained by scaling and shifting , and the function in this article is the unit ramp function (slope 1, starting at 0).