Introduction to slope presentation
- 1. Meaning of Slope Sima Javaheri & Sara Kelly
- 2. California Content Standard • 3.3 Graph linear functions, noting that the vertical change (change in y- value) per unit of horizontal change (change in x- value) is always the same and know that the ratio ("rise over run") is called the slope of a graph.
- 3. NCTM Standard • Represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic rules
- 4. Objectives of the Lesson • Given a graph of a line, students will be able to identify the slope as being positive, negative, zero, or neither. • Given a graph of a line, students will be able to calculate slope by using rise over run. • Given a two points on a line, students will be able to apply the slope formula accurately.
- 5. What is Slope??? Slope is the ratio of the vertical change to the horizontal change. In a linear relationship, it is a constant rate of change. It can also be characterized as the steepness of a line. vertical change rise y2 − y1 slope = m = = = horizontal change run x2 − x1
- 7. Positive vs. Negative Slopes • A line that moves upward from left to right has a positive slope. Hint: If you can transform the line to resemble a “P” then it is positive! • A line that moves downward from left to right has a negative slope. Hint: If you can transform the line to resemble a “N” then it is negative!
- 8. Kinds of Slopes • Positive Slope • Ne gative S lope
- 9. Zero and Neither Slope A line that is flat from left to right has a zero slope. A line that is straight up and down (vertical) has no s lope (neither).
- 10. Continued • Zero • Neither
- 11. Rise over Run rise Slope = run Rise is the vertical distance between the points Run is the horizontal distance between the points
- 12. Use Rise over Run •What is the rise value? Rise = 4 •What is the run value? Run = 1 What is the Slope? rise 4 = =4 run 1
- 13. Slope Formula • Given two points ( x1 , y1 ) and ( x2 , y2 ) , the slope can be calculated by substituting the x- and y-values into the following formula: y 2 −y1 m= x2 −x1
- 14. Example Find the slope of the line that goes through these two points (1, 1) and (2,3): 3 −1 2 m= = =2 2 −1 1
- 15. Now, you try… Given (0,4) and (2, -2), compute the slope using the slope formula: −2 −4 −6 m= = = −3 2 −0 2
- 16. References 1. Kaplan, Andrew. Math On Call. Wilmington: Houghton Mifflin, 1998. 1. Van de Walle, J, & Lovin, L, Teaching Student Centered Mathematics, Boston: Pearson (2001). 2. http://www.math.iupui.edu/~momran/m119/notes/slope