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Geometry 13.2 Slope of a Line 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. For every value of x, will there be a value of y? yes Finding Slope change in y Slope = change in x vertical change = horizontal change rise = run Subtract numerator and denominator in the same order y2 – y1 = x2 – x1 4-1 3 = = 5-3 2 ∆y ∆x 2 3 ● (5,4) ● (3,1) Example 1a: Find the slope of the line. y slope = y2 – y1 x2 – x1 = = = 4 – (-2) 5-1 6 4 3 2 . (5 , 4) x . (1 , -2) 3 __ The slope of the line is 2 Example 1b: Find the slope of the line. slope = = = y y2 – y1 x2 – x1 -5 – (-2) 3 – (- 1) -3 4 (-1 , -2) x . . (3 , -5) 3 __ The slope of the line is - 4 POSITIVE slopes rise as you move from left to right. uphill NEGATIVE slopes fall as you move from left to right. downhill Do #1 and #4 from your notes and check them below using the formula. You have one minute……. 1. m = -5/4 4. m = 2/3 uphill or downhill? uphill or downhill? Example 2a. Find the slope of the line. y slope = y2 – y1 x2 – x1 = = = 5– 5 3 – (-4) 0 3+4 . (-4 , 5) . (3 , 5) x It’s like jogging on flat ground, your slope is zero. 0 7 The slope of the line is 0. All horizontal lines have a zero slope. Example 2b. How about this slope? slope = = = y2 – y1 x2 – x1 It’s like going up in an elevator, your rise can be anything, but your run is zero. y 4 – (-1) 2-2 5 0 .(2 , 4) . (2 , -1) x The slope of the line is undefined. All vertical lines have an undefined slope. Every type of slope. Positive Slope Greater than 1 Positive Slope Less than 1 Uphill Uphill Steep Flatter Negative Slope Greater than 1 Negative Slope Less than 1 Slope = 0 Undefined Slope Running up the hill is undefined! Downhill Downhill Steep Flatter Exercise #12: Find the slope and length of AB. A (4, -2) B (5, -3) slope: -3 – (-2) -1 = m= 5-4 1 length: d = (5 - 4) +(-3 - (-2)) 2 = 1 +(-1) 2 2 2 = √2 = -1 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 a. Find 3 other points on the line that passes through P(1, 2) and has slope 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 (-2, 0) Example 3b y ). A line with slope 4/3 passes through points (4, -5) and (-2, -13 __ 4 = 3 y – (-5) 4 = 3 y+5 -6 -2 – 4 Use the slope formula to find the missing y coordinate. Simplify and solve as a proportion -24 = 3y + 15 -39 = 3y y = -13 Do Exercises #18 and #21 from your notes and check them with the answers below. 18. (7, -1) (-1, -3) (-5, -4) 19. The missing y coordinate is 4. Homework pg.