Download Solving Linear Equations

Chapter 3
Analytical Algebra 2
Rectangular Cooordinate System
Rectangular Coordinate system
Axes
Ordered pairs
x-coordinate
y-coordiante
Graph an ordered pair
Origin
Quadrants
Homework
Page 138 3, 4, 5, 6
.
Distance and Midpoint
Find the distabnce between the points:
(2, 4) and (-5, 4)
(2, -1) and (2, 3)
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Chapter 3
Analytical Algebra 2
(3, 4) and (0, 0)
(2 , 1) and (-1, 5)
The Distance Formula
Line –
Line segment –
Length of a line segment –
Midpoint –
Find the midpoint of the line segment whose indpoints are (2, 4) and (5, 4)
2
Chapter 3
Analytical Algebra 2
Find the midpoint of the line segment with endpoints ( -5, 4) and ( -3, 2)
The Midpoint Formula –
Find the midpoint of the line with endpoints (-3, -5) and (-2, 3)
Homework
Page 140 24, 27, 30
Graphs of Linear Equations
Solve y + 1 = 2x
How many solutions?
What do they look like?
How can we represent them?
3
Chapter 3
Analytical Algebra 2
Graph the equation y = -3x + 2
NOTE: When we graph an equation we are
Why is y = -3x + 2 called a linear equation?
Graph 4x – y = 4
Graph 6 + 2y = -2
Homework
Page 174 5, 6, 8, 15, 16, 17
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Chapter 3
Analytical Algebra 2
5
Graph the equation y = 4
Graph the equation x = -2
Homework
Page 175 18 - 22
Intercepts –
x-intercept –
(
,
)
y-intercept –
(
,
)
Find the x and y intercepts, if they exist, for:
To find intercepts:
y = 2x + 1
x-intercept
yintercept
1.
1.
2.
2.
3.
3.
Chapter 3
Analytical Algebra 2
Find, if they exist, the x-intercept and y-intercept for 3x + 4y = -12.
Homework
Page 175 26, 30, 33, 36
Slope
Slope of a line –
Slope Formula –
Remember our fraction rules.
Find the slope of line which passese through the points:
(2, 4) and (4, 5)
(-1, 2) and (3, -4)
6
Chapter 3
Analytical Algebra 2
Find the slope of the line which passes through thepoints:
(3, 2) and (-4, 2)
(2, 3) and (2, -4)
Every horizontal line has:
An equation of:
A slope of _______.
Every vertical line:
An equation of:
______ slope.
A line which slants downward has __________________ slope.
A line which slants upwards has ____________________ slope.
Homework
Page 186
3, 5, 7, 11, 15
Draw the graph of the line which passes through the point (-4, 2) and which has a slope of 3.
7
Chapter 3
Note : 3 = -----
Analytical Algebra 2
-4 = ----
3
 
4
=
Draw the graph of the line which passes through:
the point (0, 4) and which has a slope of 2/3.
the point (-3,0) and which has a slope of -3/4.
Graph the equation y = 5/3x – 4
We can graph by finding three ____________ / solutions.
Or
We can graph by recognizing that...
Graph the equation x + 2y = 4
3
Graph the equation y   x  4
2
Homework
Page 188
31, 33, 37, 38, 42, 44
8
Chapter 3
Analytical Algebra 2
9
More with Slopes
Horizonatl lines have _________________ slope.
Vertical lines have ____________ slope
Upward slanting lines have __________________ slopes.
Downward slating lines have _________________ slopes.
“Steep” lines have ______________________ slopes, greater than _______( in absolute value )
Slow rising lines have _____________________ slopes, less than _______ ( in absolute value )
Sketch a line with the given slopes:
3
½
-2/5
1
-1
-6
-7/2
9/4
A positive slopes means that as x increases, y ________________________, or as x decresases,
y ___________________
A negative slope means that as x increase, y _________________________, or as x decreases,
y ______________________.
Solve for x:
4 x

5 2
2 x 1
 
3
5
Chapter 3
Analytical Algebra 2
A line with a slope of 2/5 passes through the points (4, 3) and (-1, y). Find y.
A line with slope -3, passes though the points (x, 3) and (0, 6). Find x.
a line passes through the points ( -4, 7) , (4 , 1) and ( x , 4). Find x.
Homework
Page 189 47 – 53
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Chapter 3
Analytical Algebra 2
11
Writing Equations of Lines
y = 2x + 3
2x – 3y = 9
x = 4y – 7
2x – 3 + 3y = 4x – 7y + 10
y – 3 = 2(x + 4) x2 – y = 9
There are a few different forms of a line that we can use, we will focus on tow of them.
Slope-intercpt form
Point-slope form
Standard form
Write an equation of the line:
Passing through the point (0, 3) with a slope of 4.
Passing through the point (2, 0) with a slope of -2/3
Chapter 3
Analytical Algebra 2
Passing through the point (-2, 4) with m = -4
Passing through the points (0, 4) and (3, 5).
Passing through the points (-1, 1) and (4, 4)
Homework
Page 194
3, 5, 7, 11, 17, 29, 37, 38
Graph the line y = 4
Wirte the equation of the line which passes through the
point (2, 4) and has slope = 0.
12
Chapter 3
Analytical Algebra 2
Write the equation of the line which passes through the point (-2 , 4) and has no slope.
Write the equation of the line which passes through the points (-2, 3) and (4, 3).
Write the equation of the line which passes through the points (-2, 3) and (-2, 3).
All horizontal lines, lines with a slope of ________________, have equations:
All vertical lines, lines with ____________ slope, have equations :
Homework
Page 195
19, 21, 25, 43, 47, 49
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Chapter 3
Analytical Algebra 2
Parallel and Perpendicular Lines
In geometry:
Parallel lines
Perpendicular lines
In algebra:
Parallel lines
Perpenduclar lines
Are the lines, one passing though the points (-2, 1) and (-5, -1) and the other passing through the
points (1, 0) and (4, 2), parallel, perpendicular, neither or both?
14
Chapter 3
Analytical Algebra 2
Are the graphs of the lines, y= 3/2x – 5 and 2x + 3y = 6, parallel, perpendicular or netiher?
Write an equation of a line perpendicular to the line y = 4x + 5, which passes through (0, 2).
Write a n equation of the line which passes through the point (2, 3) and which is parallel to the
line y = 1/2x – 4.
Write the equation of the line which passes through the point (3, -4) and which is perpendicular
to the line 2x – y = -3.
15
Chapter 3
Analytical Algebra 2
What slope does a line have, which is perpendicular to a line with slope of 0 have?
Write the equation of the line which is parallel to the line x = 5 and which passes thorugh the
point (3, 1).
Write the equation of the line which is perpendicular, to the line x = 5 and which passes through
the point (5, 2).
Homework
Page 203
3, 5, 11, 13, 19, 21, 23, 27, 29
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Chapter 3
Analytical Algebra 2
How many solutions does y + 4 = 3 have?
How many solutions does y = x – 1 have?
How many solutions does y > x – 1 have?
The graph of the solutions to y = x – 1 creates a _____________.
The graph of the solutions to y > x – 1 creates a ______________.
Graph y > x – 1
Graph x – 2y ≤ 4
17
Chapter 3
Graph y < -x + 2
Analytical Algebra 2
Graph x > -1
Graph y ≤ 3
Homework
Page 209 11, 13, 14, 19, 20
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