Download Freeslope

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
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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
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Merrill, Algebra 1 Book, Chapter 10, pages 398-437
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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
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http://www.chacha.com/question/what-is-the-definition-of-a-zero-slope
http://glossary.econguru.com/economic-term/zero+slope
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http://www.mathopenref.com/coordslope.html
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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