Slope - Revision history

Lila: /* Resources */

2021-09-20T18:50:38Z

Resources

2021-09-20T18:49:02Z

Slope Between Two Points

2021-09-20T18:48:28Z

Point-Slope Form

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Slope-Intercept Form

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Resources

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Slope-Intercept Form

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Point-Slope Form

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Point-Slope Form

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Slope Between Two Points

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Slope Between Two Points

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 ==Resources==
 * [https://tasks.illustrativemathematics.org/content-standards/tasks/1537 Slope Between Points], Illustrative Mathematics
 * [https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:forms-of-linear-equations/x2f8bb11595b61c86:summary-forms-of-two-variable-linear-equations/a/forms-of-linear-equations-review Forms of Linear Equations], Khan Academy

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 ===Slope Between Two Points===
-Given two points <math> (x_1, y_1) </math> and <math> (x_2, y_2) </math>, the slope between these two points is <math> m = \frac{y_2 - y_1}{x_2 - x_1}</math>. 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 <math> \frac{6 - 3}{5 - 1} = \frac{3}{4}</math>. The slope between (-1, -1) and (15, -21) is <math> \frac{-21 - (-1)}{15 - (-1)} = \frac{-21 + 1}{15 + 1} = \frac{-20}{16} = \frac{-5}{4}</math>.
+Given two points <math> (x_1, y_1) </math> and <math> (x_2, y_2) </math>, the slope between these two points is <math> m = \frac{y_2 - y_1}{x_2 - x_1}</math>. 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 <math> \frac{6 - 3}{5 - 1} = \frac{3}{4}</math>. The slope between (-1, -1) and (15, -21) is <math> \frac{-21 - (-1)}{15 - (-1)} = \frac{-21 + 1}{15 + 1} = -\frac{20}{16} = -\frac{5}{4}</math>.
 ===Point-Slope Form of a Line===

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 Given two points <math> (x_1, y_1) </math> and <math> (x_2, y_2) </math>, the slope between these two points is <math> m = \frac{y_2 - y_1}{x_2 - x_1}</math>. 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 <math> \frac{6 - 3}{5 - 1} = \frac{3}{4}</math>. The slope between (-1, -1) and (15, -21) is <math> \frac{-21 - (-1)}{15 - (-1)} = \frac{-21 + 1}{15 + 1} = \frac{-20}{16} = \frac{-5}{4}</math>.
-===Point-Slope Form===
+===Point-Slope Form of a Line===
 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>.

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 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 of a Line===
 Another form of an equation of a line is slope-intercept form. The equation of a line with a y-intercept of b (that is, a line that intersects the y-axis at the point (0, b)) and a slope of m is <math> y = mx + b </math>. For example, the equation of a line with a y-intercept of 5 and slope of 6 is <math> y = 5x + 6 </math>. Note that this equation is equivalent to point-slope form. A line with a y-intercept of 5 goes through the point (0, 5), so the point-slope form of this same line is <math> y - 5 = 6(x - 0) = 6x </math>. By adding 5 to each side of the equation, we get the slope-intercept form of the line.

← Older revision		Revision as of 18:46, 20 September 2021
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	==Resources==		==Resources==
	* [https://tasks.illustrativemathematics.org/content-standards/tasks/1537 Slope Between Points], Illustrative Mathematics		* [https://tasks.illustrativemathematics.org/content-standards/tasks/1537 Slope Between Points], Illustrative Mathematics
		+	* [https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:forms-of-linear-equations/x2f8bb11595b61c86:summary-forms-of-two-variable-linear-equations/a/forms-of-linear-equations-review Forms of Linear Equations], Khan Academy

← Older revision		Revision as of 18:36, 20 September 2021
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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{-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===