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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 y-intercept in a given situation; - PowerPoint PPT Presentation
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Cissie HamlinCissie Hamlin
EDAT 6119, Spring 2010Slippery Slope
EDAT 6119, Spring 2010Slippery 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;
• 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.
Types of Slope
U
nd
efin
ed
Zero Slope
P
ositi
ve s
lope Negative 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 – y1 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: y2 – y1
X2-X1
• Standard Formula of a line: Ax+By=C
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.
• How to find x and y intercept with out much math!
• X- intercept is c/b• Y- intercept is c/a
Shortcut!
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
• 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 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)
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/HCPSAlgebra1/module6review.html
Slope Practice
• http://www.algebrahelp.com/worksheets/view/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