cissie hamlin edat 6119, spring 2010 slippery slope edat 6119, spring 2010 slippery slope

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