Graphing Linear Equations and Inequalities: Exercise Supplement
m22004
Graphing Linear Equations and Inequalities: Exercise Supplement
1.5
2009/03/04 03:17:24 US/Central
2009/06/01 11:01:27.862 GMT-5
Wade
Ellis
Wade Ellis
fgafaculty@gmail.com
Denny
Burzynski
Denny Burzynski
denny_burzynski@westvalley.edu
Wade
Ellis
Wade Ellis
fgafaculty@gmail.com
Denny
Burzynski
Denny Burzynski
denny_burzynski@westvalley.edu
LearningMate
LearningMate
LearningMate LearningMate
abhijit.chaturvedi@learningmate.com
Matt
Gardner
Matt Gardner
mgardner@wordsandnumbers.com
Wade
Ellis
Wade Ellis
fgafaculty@gmail.com
Denny
Burzynski
Denny Burzynski
denny_burzynski@westvalley.edu
algebra
elementary
Mathematics and Statistics
This module is from Elementary Algebra by Denny Burzynski and Wade Ellis, Jr.
In this chapter the student is shown how graphs provide information that is not always evident from the equation alone. The chapter begins by establishing the relationship between the variables in an equation, the number of coordinate axes necessary to construct its graph, and the spatial dimension of both the coordinate system and the graph. Interpretation of graphs is also emphasized throughout the chapter, beginning with the plotting of points. The slope formula is fully developed, progressing from verbal phrases to mathematical expressions. The expressions are then formed into an equation by explicitly stating that a ratio is a comparison of two quantities of the same type (e.g., distance, weight, or money). This approach benefits students who take future courses that use graphs to display information.
The student is shown how to graph lines using the intercept method, the table method, and the slope-intercept method, as well as how to distinguish, by inspection, oblique and horizontal/vertical lines.
This module contains the exercise supplement for the chapter "Graphing Linear Equations and Inequalities in One and Two Variables".
en
Exercise Supplement
Graphing Linear Equations and Inequalities in One Variable (<link document="m18877"/>)
For the following problems, graph the equations and inequalities.
6x−18=6
x=4
4x−3=−7
5x−1=2
x=
3
5
10x−16<4
−2y+1≤5
y≥−2
−7a
12
≥2
3x+4≤12
x≤
8
3
−16≤5x−1≤−11
0<−3y+9≤9
0≤y<3
−5c
2
+1=7
Plotting Points in the Plane (<link document="m21993"/>)
Draw a coordinate system and plot the following ordered pairs.
(3,1),(4,−2),(−1,−3),(0,3),(3,0),(
5,−
2
3
)
As accurately as possible, state the coordinates of the points that have been plotted on the graph.
Graphing Linear Equations in Two Variables (<link document="m21995"/>)What is the geometric structure of the graph of all the solutions to the linear equation
y=4x−9
?
a straight line
Graphing Linear Equations in Two Variables (<link document="m21995"/>) - Graphing Equations in Slope-Intercept Form (<link document="m22000"/>)For the following problems, graph the equations.
y−x=2
y+x−3=0
−2x+3y=−6
2y+x−8=0
4(x−y)=12
3y−4x+12=0
y=−3
y−2=0
x=4
x+1=0
x=0
y=0
The Slope-Intercept Form of a Line (<link document="m22014"/>)
Write the slope-intercept form of a straight line.
The slope of a straight line is a of the steepness of the line.
measure
Write the formula for the slope of a line that passes through the points
(
x
1
,y
)
1
and
(
x
2
,y
)
2
.
For the following problems, determine the slope and
y-intercept
of the lines.
y=4x+10
slope: 4
y-intercept: (
0,10
)
y=3x−11
y=9x−1
slope: 9
y-intercept: (
0,−1
)
y=−x+2
y=−5x−4
slope: −5
y-intercept: (
0,−4
)
y=x
y=−6x
slope: −6
y-intercept: (
0,0
)
3y=4x+9
4y=5x+1
slope:
5
4
y-intercept: (
0,
1
4
)
2y=9x
5y+4x=6
slope: −
4
5
y-intercept: (
0,
6
5
)
7y+3x=10
6y−12x=24
slope: 2
y-intercept: (
0,4
)
5y−10x−15=0
3y+3x=1
slope: −1
y-intercept: (
0,
1
3
)
7y+2x=0
y=4
slope: 0
y-intercept: (
0,4
)
For the following problems, find the slope, if it exists, of the line through the given pairs of points.
(5,2),
(6,3)
(8,−2),
(10,−6)
slope: −2
(0,5),
(3,4)
(1,−4),
(3,3)
slope:
7
2
(0,0),
(−8,−5)
(−6,1),
(−2,7)
slope:
3
2
(−3,−2),
(−4,−5)
(4,7),
(4,−2)
No Slope
(−3,1),
(4,1)
(
1
3
,
3
4
),(
2
9
,−
5
6
)
slope:
57
4
Moving left to right, lines with slope rise while lines with slope decline.
Compare the slopes of parallel lines.
The slopes of parallel lines are equal.
Finding the Equation of a Line (<link document="m21998"/>)For the following problems, write the equation of the line using the given information. Write the equation in slope-intercept form.
Slope=4,
y-intercept=5
Slope=3,
y-intercept=−6
y=3x−6
Slope=1,
y-intercept=8
Slope=1,
y-intercept=−2
y=x−2
Slope=−5,
y-intercept=1
Slope=−11,
y-intercept=−4
y=−11x−4
Slope=2,
y-intercept=0
Slope=−1,
y-intercept=0
y=−x
m=3,
(4,1)
m=2,
(1,5)
y=2x+3
m=6,
(5,−2)
m=−5,
(2,−3)
y=−5x+7
m=−9,
(−4,−7)
m=−2,
(0,2)
y=−2x+2
m=−1,
(2,0)
(2,3),
(3,5)
y=2x−1
(4,4),
(5,1)
(6,1),
(5,3)
y=−2x+13
(8,6),
(7,2)
(−3,1),
(2,3)
y=
2
5
x+
11
5
(−1,4),
(−2,−4)
(0,−5),
(6,−1)
y=
2
3
x−5
(2,1),
(6,1)
(−5,7),
(−2,7)
y=7 (
zero slope
)
(4,1),
(4,3)
(−1,−1),
(−1,5)
x=−1 (
no slope
)
(0,4),
(0,−3)
(0,2),
(1,0)
y=−2x+2
For the following problems, reading only from the graph, determine the equation of the line.
y=
2
3
x−2
y=−2
y=1
Graphing Linear Inequalities in Two Variables (<link document="m22011"/>)For the following problems, graph the inequalities.
y≤x+2
y<−
1
2
x+3
y>
1
3
x−3
−2x+3y≤−6
2x+5y≥20
4x−y+12>0
y≥−2
x<3
y≤0