Difference between revisions of "Slope"
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| − | Slope is the steepness of a line. A positive slope rises; a negative slope falls. Another term for slope is gradient. | + | '''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): | 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): | ||
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:: <math>m = \frac{\Delta y}{\Delta x}</math> | :: <math>m = \frac{\Delta y}{\Delta x}</math> | ||
| − | 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. | + | 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: | For a straight line, another way of representing the slope (m) is as follows: | ||
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where the two points are located at (x<sub>1</sub>, y<sub>1</sub>) and (x<sub>2</sub>, y<sub>2</sub>). | where the two points are located at (x<sub>1</sub>, y<sub>1</sub>) and (x<sub>2</sub>, y<sub>2</sub>). | ||
| − | [[ | + | ==Introduction to derivative== |
| − | [[Category: | + | |
| + | If a function has value <math>f(x)</math> at <math>x</math> and <math>f(x+h)</math> at <math>x+h</math> with <math>h>0</math> than the slope of the line joining <math>(x,f(x))</math> to <math>(x+h,f(x+h))</math> is, | ||
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| + | :<math>\frac{f(x+h)-f(x)}{h}</math>. | ||
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| + | The slope of the line that meets (is tangential to) <math>f(x)</math> at <math>x</math> is the limit as <math>h</math> tends to zero, or, | ||
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| + | :<math>\lim_{h\rightarrow0}\frac{f(x+h)-f(x)}{h},</math> | ||
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| + | which is denoted <math>f'(x)</math>, which is called the [[Derivative (calculus)|derivative]] of <math>f(x)</math>. | ||
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| + | [[Category:Algebra]] | ||
Latest revision as of 21:08, September 8, 2020
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):
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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:
where the two points are located at (x1, y1) and (x2, y2).
Introduction to derivative
If a function has value Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f(x)} at and at with than the slope of the line joining to is,
- .
The slope of the line that meets (is tangential to) at is the limit as tends to zero, or,
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \lim_{h\rightarrow0}\frac{f(x+h)-f(x)}{h},}
which is denoted Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f'(x)} , which is called the derivative of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f(x)} .