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Understanding Slope in Geometry: Review of Lines and Finding Slope

Learn about the slope of a line, determining points on a line, and the formula for finding slope. Practice examples and exercises to enhance your understanding of positive, negative, zero, and undefined slopes in geometry.

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Understanding Slope in Geometry: Review of Lines and Finding Slope

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  1. Geometry 13.2 Slope of a Line

  2. Review of Lines: 1. How many points determine a line? 2 2. How many points are on a line? an infinite number of points

  3. ∆y Finding Slope ∆x change in y Slope = 2 change in x ● (5,4) 3 vertical change ● = (3,1) horizontal change Subtract numerator and denominator in the same order rise = run y2 – y1 4 - 1 3 = = = x2 – x1 5 - 3 2

  4. Example 1a: Find the slope of the linewithout graphing. y2 – y1 . y slope = x2 – x1 (5, 4) 4– (-2) = 5 - 1 x . 6 = (1, -2) 4 3 = 3 __ 2 The slope of the line is 2

  5. Example 1b: Find the slope of the line. y y2 – y1 slope = x2 – x1 -5– (-2) = 3 – (- 1) . x (-1, -2) - 3 = 4 . (3, -5) 3 __ - The slope of the line is 4

  6. POSITIVE slopes rise as you move from left to right. uphill NEGATIVE slopes fall as you move from left to right. downhill Try #1 and #4 from your notes and check them below using the formula. 1. Find m. uphill or downhill? 1. m = -5/4 4. Find m. uphill or downhill? 4. m = 2/3

  7. Example 2a. Find the slope of the line. y2 – y1 y slope = . . x2 – x1 5– 5 (-4, 5) (3, 5) = 3 – (-4) x It’s like jogging on flat ground, your slope is zero. 0 = 3 + 4 0 = The slope of the line is 0. 7 All horizontal lines have a zero slope.

  8. Example 2b. How about this slope? It’s like going up in an elevator, your rise can be anything, but your run is zero. y2 – y1 . y slope = (2, 4) x2 – x1 4– (-1) = 2 - 2 . x (2, -1) 5 = 0 The slope of the line is undefined. All vertical lines have an undefined slope.

  9. Every type of slope. Positive Slope Positive Slope Slope = 0 Greater than 1 Less than 1 Uphill Uphill Steep Flatter Negative Slope Undefined Slope Negative Slope Less than 1 Greater than 1 Running up the hill is undefined! Downhill Downhill Flatter Steep

  10. y y y y y O O x x O O x x O x Does the slope of the line appear to be positive, negative, zero, or not defined? ZERO UNDEFINED NEGATIVE POSITIVE POSITIVE

  11. Exercise #12: Find the slope and length of AB. A (4, -2) B (5, -3) -3 – (-2) -1 = -1 = m = slope: 5 - 4 1 d = length: = = √2

  12. The slope of a line segment is constant. No matter which two points you choose on the line, you will get the same value for m. You can use this property to find other points on the same line. • Example 3a • Find 3 other points on the line that passes through P(1, 2) and has slope . Try it without a graph first. 2/3. Plot the point (1,2). • • From there, rise 2 and run 3 to get another point. • • (4, 4) From there, rise 2 and run 3 to get another point. (7, 6) You can also go back to (1,2) and from there rise -2 and run -3 to get to the point (0, -2)

  13. Example 3b A line with slope 4/3 passes through points (4, -5) and (-2, __ ). y -13 Use the slope formula to find the missing y coordinate. y – (-5) 4 = Simplify and solve as a proportion 3 -2 – 4 y + 5 -24 = 3y + 15 4 = -6 -39 = 3y 3 y = -13

  14. Do Exercises #18 and #21 from your notes and check them with the answers below. 18. • A line with m = 3/8 • goes through (-1, 1) and (7, __ ) 18. (7, -1) (-1, -3) (-5, -4) 21. The missing y coordinate is 4.

  15. Homework P. 531-533 CE 1-3, 6 WE 1-25 Odd

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