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Cissie Hamlin

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

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Cissie Hamlin

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  1. Cissie Hamlin 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. How to use coordinates 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: y2– y1 X2-X1

  13. How to use coordinates to find the slope Example: (2,6), (4,8) (x,y), (x,y) y2– y18-62 X2-X1 = 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: y2 – y1 X2-X1 • 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. Shortcut! • How to find x and y intercept with out much math! • X- intercept is c/b • Y- intercept is c/a

  19. Slope • Slope-Intercept Form • y=mx+b • Slope is m • y-intercept is b • 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 y-intercept l let x = 0 3x -2y = 12 3(0) – 2y = 12 -2y = 12 y = -6 To find the x-intercept let y = 0 3x – 2y = 12 3x – 2(0) = 12 3x = 12 x = 4 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/HCPSAlgebra1/module6review.html

  25. Slope Practice • http://www.algebrahelp.com/worksheets/view/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

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