Slope

From Conservapedia

Slope is the steepness of a line. A positive slope rises; a negative slope falls. Another term for slope is gradient.

For a straight line, the slope (m) is constant and represented by the difference in the vertical direction (y) divided by the difference in the horizontal direction (x):

$m = \frac{\Delta y}{\Delta x}$

The delta, Δ, represents the difference in values between any two points in the x or y direction for straight line. For a curve, the delta, Δ, represents the difference in values for two points in very close proximity to each other.

For a straight line, another way of representing the slope (m) is as follows:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

where the two points are located at (x₁, y₁) and (x₂, y₂).

Introduction to derivative

If a function has value $f (x)$ at $x$ and $f (x + h)$ at $x + h$ with $h > 0$ than the slope of the line joining $(x, f (x))$ to $(x + h, f (x + h))$ is,

$\frac{f(x+h)-f(x)}{h}$ .

The slope of the line that meets (is tangential to) $f (x)$ at $x$ is the limit as $h$ tends to zero, or,

$\lim_{h\rightarrow0}\frac{f(x+h)-f(x)}{h},$

which is denoted $f'(x)$ , which is called the derivative of $f (x)$ .

Slope

From Conservapedia

Introduction to derivative

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