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