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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 yintercept in a given situation; • C. Graph equations of the form y = mx + b; • D. Graph equations of the form Ax + By = C; Slope • What is it? The ratio of rise to run. Find the slope of this line. m=slope m= 3 5 4 Types of Slope • • • • Positive Slope Negative Slope 0 – Slope Undefined Slope Positive slope A positive slope rises right. Negative slope A negative slope falls right. 0-slope A 0-slope is a horizontal line.(0/2) Zero in the numerator. Undefined Slope An undefined slope is a vertical line. (2/0) Zero in the denominator. Undefined Types of Slope Zero Slope 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. 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 • 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 – y 1 X2-X1 • Example: (2,6), (4,8) (x,y), (x,y) y2 – y1 8-6 2 X2-X1 = 4-2 = 2 = 1 • Therefore, the slope is 1. We would write this as m=1. Fun Facts • A horizontal line is ALWAYS zero. • A vertical line is ALWAYS undefined. • Slope intercept form: y=mx+b • Formula for slope: y–y X -X • Standard Formula of a line: Ax+By=C 2 2 1 1 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. Practice for you. • y=2x+5 • 3y+9x=27 Slope as a rate of change This graph represents the rate at which y and x change. Shortcut! • How to find x and y intercept with out much math! • X- intercept is c/b • Y- intercept is c/a Slope Standard Form Slope-Intercept Form • y=mx+b •Slope is m •y-intercept is b •Ax+By=C •Slope is –A/B •y-intercept is C/B • 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. • Let’s graph the equation 3x – 2y = 12 using the x- and y-intercepts. To find the y-intercept To find the x-intercept l let x = 0 Let’s graph it using the let y = 0 3x – 2y = 12 3x – 2(0) = 12 3x = 12 x=4 points (4, 0) and (0, -6) 3x -2y = 12 3(0) – 2y = 12 -2y = 12 y = -6 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 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. Games • http://teachers.henrico.k12.va.us/math/HCPS Algebra1/module6review.html Slope Practice • http://www.algebrahelp.com/worksheets/vie w/graphing/slope.quiz 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