Difference between revisions of "Slope"
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===Point-Slope Form=== | ===Point-Slope Form=== | ||
| − | The equation for a line with a slope of <math> m </math> that goes through some point <math> (x_1, y_1) </math>, in point-slope form, is <math> y - y_1 = m(x - x_1) </math>. For example, the equation of a line with a slope of 3 that goes through the point (1, 4) is <math> y - 4 = 3(x - 1) </math>. The equation of a line with a slope of <math> \frac{ | + | The equation for a line with a slope of <math> m </math> that goes through some point <math> (x_1, y_1) </math>, in point-slope form, is <math> y - y_1 = m(x - x_1) </math>. For example, the equation of a line with a slope of 3 that goes through the point (1, 4) is <math> y - 4 = 3(x - 1) </math>. The equation of a line with a slope of <math> -\frac{1}{2} </math> that goes through point (-7, -7) is <math> y + 7 = -\frac{1}{2}(x + 7) </math>. |
===Slope-Intercept Form=== | ===Slope-Intercept Form=== | ||
Revision as of 12:37, 20 September 2021
Slope Between Two Points
Given two points 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 (x_1, y_1) } and 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 (x_2, y_2) } , the slope between these two points is 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{y_2 - y_1}{x_2 - x_1}} . That is, the slope between two points is the difference between the y-coordinates of the points, divided by the difference between the x-coordinates of the points. For example, the slope between the two points (1, 3) and (5, 6) is 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 \frac{6 - 3}{5 - 1} = \frac{3}{4}} . The slope between (-1, -1) and (15, -21) is 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 \frac{-21 - (-1)}{15 - (-1)} = \frac{-21 + 1}{15 + 1} = \frac{-20}{16} = \frac{-5}{4}} .
Point-Slope Form
The equation for a line with a slope 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 m } that goes through some point 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 (x_1, y_1) } , in point-slope form, is 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 y - y_1 = m(x - x_1) } . For example, the equation of a line with a slope of 3 that goes through the point (1, 4) is 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 y - 4 = 3(x - 1) } . The equation of a line with a slope 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 -\frac{1}{2} } that goes through point (-7, -7) is 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 y + 7 = -\frac{1}{2}(x + 7) } .
Slope-Intercept Form
Resources
- Slope Between Points, Illustrative Mathematics
