1. Cissie Hamlin EDAT 6119, Spring 2010 Slippery Slope EDAT 6119, Spring 2010 Slippery Slope

2. M8A4. Students will graph and analyze graphs of linear equations and inequalities A. Interpret slope as a rate of change; B. Determine the meaning of the slope and y- intercept in a given situation; C. Graph equations of the form y = mx + b; D. Graph equations of the form Ax + By = C;

3. Slope What is it? The ratio of rise to run. Find the slope of this line. m=slope m= 3 5

4. 4 Types of Slope Positive Slope Negative Slope 0 – Slope Undefined Slope

5. Positive slope A positive slope rises right.

6. Negative slope A negative slope falls right.

7. 0-slope A 0-slope is a horizontal line.(0/2) Zero in the numerator.

8. Undefined Slope An undefined slope is a vertical line. (2/0) Zero in the denominator.

9. Types of Slope Undefined Zero Slope Positive slope Negative Slope

10. Slope You can find the slope of a line that passes through two given points using the slope formula. y₂ - y₁ x₂ - x₁ Plug in the values for y and x then do the math.

11. Slope The slope of a line tells how steep the change is as you follow the line from left to right Rise Run Change in y vertical change Change in x horizontal change y₂ - y₁ x₂ - x₁

12. You can find the slope and graph the slope just by using the coordinates. To find the slope using the x and y coordinates, you have to use the formula: y 2 – y 1 X 2 -X 1

13. Example: (2,6), (4,8) (x,y), (x,y) y 2 – y 1 8-6 2 X 2 -X 1 = 4-2 = 2 = 1 Therefore, the slope is 1. We would write this as m=1.

14. Fun Facts A horizontal line is ALWAYS zero. A vertical line is ALWAYS undefined. Slope intercept form: y=mx+b Formula for slope: y 2 – y 1 X 2 -X 1 Standard Formula of a line: Ax+By=C

15. Fun Facts Continued The slope of a line tells how steep the line is. The greater the absolute value of the slope, the steeper the line. The smaller the absolute value of the slope, the flatter the line.

16. Practice for you. y=2x+5 3y+9x=27

17. Slope as a rate of change  This graph represents the rate at which y and x change.

18. How to find x and y intercept with out much math! X- intercept is c/b Y- intercept is c/a Shortcut!

19. Slope-Intercept Form y=mx+b Slope is m y-intercept is b Slope Standard Form Ax+By=C Slope is –A/B y-intercept is C/B

20. Compare the slope intercept form of a linear equation with the standard form, Ax + By = C, solve for y. By = -Ax + C y = -Ax/B + C/B slope y-intercept Therefore, the slope is -A/B and the y-intercept is C/B.

21. Let’s graph the equation 3x – 2y = 12 using the x- and y-intercepts. To find the x-intercept let y = 0 3x – 2y = 12 3x – 2(0) = 12 3x = 12 x = 4 To find the y-intercept l let x = 0 3x -2y = 12 3(0) – 2y = 12 -2y = 12 y = -6 Let’s graph it using the points (4, 0) and (0, -6)

22. Vocabulary 0-slope: A line on a graph that is horizontal. Undefined slope: A line on a graph that is vertical Rise: The vertical distance of the slope. Run: The horizontal distance of the slope. Slope: the ratio of rise to run. Slope-intercept form: y=mx+b Standard form: ax+by=c

23. Vocabulary X-intercept: the x-coordinate of a point where a line, curve, or surface intersects the x-axis. Y-intercept : the y-coordinate of a point where a line, curve, or surface intersects the y-axis. Point-slope form- y-y =m(x-x ) Linear Relationship: A set of ordered pairs that form a straight line.

24. Games http://teachers.henrico.k12.va.us/math/HCPS Algebra1/module6review.html http://teachers.henrico.k12.va.us/math/HCPS Algebra1/module6review.html

25. Slope Practice http://www.algebrahelp.com/worksheets/vie w/graphing/slope.quiz http://www.algebrahelp.com/worksheets/vie w/graphing/slope.quiz

26. Resources Merrill, Algebra 1 Book, Chapter 10, pages 398-437 http://algebralab.org/studyaids/studyaid.aspx?file=Algebra1_5-5.xml http://sk19math.blogspot.com/2007/04/graphing-standard-form-of-equation.html http://www.math.com/school/subject2/images/S2U4L1GLgrid.gif http://courses.wccnet.edu/~palay/precalc/22mt01.htm http://www.nsa.gov/academia/_files/collected_learning/middle_school/algebra/interpreting_slope.pdf http://cs.explorelearning.com/docs/qz_slope-int.pdf http://www.purplemath.com/modules/slope.htm http://www.mathwords.com/xyz/zero_slope.htm http://www.chacha.com/question/what-is-the-definition-of-a-zero-slope http://glossary.econguru.com/economic-term/zero+slope http://www.mathwords.com/u/undefined_slope.htm http://www.wtamu.edu/academic/anns/mps/math/mathlab/int_algebra/int_alg_tut15_slope.html http://www.mathopenref.com/coordslope.html http://en.wikipedia.org/wiki/Linear_equation#Standard_form http://mathforum.org/library/drmath/view/57137.html http://www.math-glossary.info/definition/2669-Standard_Form http://www.merriam-webster.com/netdict/slope-intercept%20form http://www.computerhope.com/jargon/x/xaxis.htm http://library.thinkquest.org/2647/geometry/glossary.htm http://dictionary.reference.com/browse/coordinate%20plane http://www.algebra-class.com/rate-of-change.html http://regentsprep.org/REgents/math/ALGEBRA/AC1/Rate.htm http://courses.wccnet.edu/~palay/precalc/22mt01.htm