SLOPE

1. SLOPE

2. SLOPE • Slope is the “tilt” of the line. • Slope is the “slant” of the line. zero slope Positive slope Positive correlation Negative slope Negative correlation undefined slope

3. SLOPE • Slope is the steepness of the “slant” of the line. • Slope is the steepness of a mountain side. • Slope is the steepness of a wheelchair ramp. • Slope is the steepness of a flight of stairs. • Slope is the steepness of a plane’s decent. • Slope is the steepness of a ski run. • Slope is steepness of a skate board ramp.

4. SLOPE • These different slopes can be measured and represented mathematically with a ratio. • This ratio can be found by going from one point on the line to another point by counting the vertical change and the horizontal change. • This ratio or slope is sometimes called the rise (vertical change) over the run (horizontal change).

5. 5 3 Let’s investigate the steepness of this mountain slope. #1) Pick two points on the side of the mountain. #2) Draw an imaginary grid. #3) Count vertically and then horizontally from one point to the other. 1 2 3 4 5 vertically horizontally 1 2 Slope = 3

6. 5 3 SLOPE There are different names for the slope ratio. 5 vertical change = horizontal change 3 5 rise = run 3 5 change in y = Slope = change in x 3

7. Slope = - Slope = 5 3 5 3 Let’s look at the “sign” of the slope or the correlation. “Going up the mountain.” positive slope “Going down the mountain.” negative slope

8. Counting Slope Negative Slope Positive Slope Counting up … rise and right … run Counting up … rise and left … run Counting down… rise and left … run Counting down… rise and right … run + / + = + -/- = + +/ - = - -/ + = -

9. Slope= + 3 5 Finding slope on the coordinate plane. +5 y 1) Plot points (2, 4) 2) Draw line +3 3) Count - - vertically (-3, 1) x 4) Count - - horizontally 5) Write slope - as a ratio

10. +4 -6 -2 3 Finding slope on the coordinate plane. y 1) Plot points 2) Draw line -6 3) Count - - vertically (-1, 2) +4 x 4) Count - - horizontally 5) Write slope - as a ratio Slope= = (5, -2)

11. Find slope algebraically when given two points Point 1: (x1, y1) Point 2: (x2, y2) difference between the y coordinates difference between the x coordinates Slope=

12. - 4 6 - 2 3 Find slope algebraically when given two points Point 1: (-1, 2) Point 2: (5, -2) difference between the y coordinates difference between the x coordinates Slope= -2 - 2 5 - -1 m= = =

13. Example 1: • Find the slope of the line containing the points (6, 7) and (8, 3) • Remember each ordered pair is (x, y) • Write slope formula • Substitute into slope formula • Subtract the y coordinates • Subtract the x coordinates m = -2

14. Example 2: • Find the slope of a line containing (-3, 6) and (-12, -9)

15. 4 1 Example 3: Through the given point, (-4, -2), graph the line with a slope of 4. y 1) Plot point 2) Count slope +1 a) Count - - vertically (-3, 2) b) Count - - horizontally +4 x m= + 5) Plot new . point (-4, -2) 6) Draw line

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