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Algebra 1
Lesson- Midpoint of a line Segment
Name:__________________________________________
Date:___________________________________________
Objective- To learn to find the midpoint of a line segment
In your own words define Midpoint:
Ex 1: Plot the given points: A(5,3) and B(3,7)
a. Visually determine the midpoint.
b. Determine a formula or equation that you can use to find midpoints under any circumstances.
General Rule for Midpoints:
Ex 2: Given the Quadrilateral ABCD, A(0,0), B(6,8), C(16,8), D(10,0)…
a. Draw ABCD
b. If R is the midpoint of side AB & S is the midpoint of side BC & T is the midpoint of side AD, draw
triangle RST
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Algebra 1
Midpoint Worksheet
Name:___________________________________
Date:____________________________________
Do each of the following on Graph paper.
1) Graph the points A (1, 6) and B (9, 6). Find the midpoint of AB visually.
2) Graph the points C (2, 2) and D (6, 2). Find the midpoint of CD visually.
3) Graph the points E (11, 9) and F (11, 3). Find the midpoint of EF visually.
Find the midpoint for each line segment using the formula.
4)
G (6, 5) and H (9, 2)
5)
I (1, 1) and J (-3, -3)
6)
K (1, -1) and L (8, -7)
7)
M (9, 3) and N (-5, -2)
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Algebra 1
Lesson- Slope and Collinearity
Name:____________________________________
Date:_____________________________________
Objective: To find the slope of a line visually and using the formula. To determine if a set of points are
collinear
In your own words, define slope:
General Definition:
Ex 1: find the slope of the line containing the points (5,4) and (3,1) visually.
General Slope Equation:
Ex 2: find the slope of the line containing the points (2,3) and (5,1) using the General Slope Equation
What does it mean to have a POSITIVE slope?
What does it mean to have NEGATIVE slope?
The following is an example of a line that has ZERO slope.
Ex: Find the slope of the line connecting the points (5,3) and (7,3)
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The following is an example of a line that has NO slope.
Ex 3: Find the slope of the line connecting the points (3,-5) & (3,5)
Collinearity
**Three points are collinear if the slopes of any two points are
equal.
Ex 4. Are the following points collinear?
(2,2) (4,3) (8,5)
Ex 5. Draw a line with the given point and slope in problems a
b. Put both lines on the same graph.
a. (0,3) , m=1
b. (-3,5) , m=-1/2
and
Ex 6: A(1,0), B(3,6), C(9,4) are the vertices of ABC
a. Find all slopes
b. D,E,F are the midpoints of sides AB, BC, CA respectively.
c. Find the slopes of sides AE, BF, CD
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Algebra 1
Lesson: Graphing Linear Equations
Name:____________________________________
Date:_____________________________________
Objective:
To be able to use the table method to graph linear equations. To be able to graph a linear
equation using only the slope and y-intercept.
Graph the following linear equations
1.
y  3x  2
2.
3x  2 y  4
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Slope-intercept form of a linear equation:
Ex 1: x + 2y – 6 = 0
Process:
a. Solve the equation for y and put into slope-intercept form
b. The value attached to the x is the slope and the value that is alone is your y intercept.
c. Identify the slope and the y-intercept.
d. Plot the y-intercept and use the slope of the line to graph the line.
Calculator Approach
2nd
y=
Input equation
Zoom
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2nd
Graph
Verify your answers to #1&2 above
Activity- Counts as a 20 point “Independent Work” Assignment.
On the graph paper provided:
1.
Create 1 large set of axes (label clearly)
2.
Graph each of the following equations using a different color for each
a. y  2 x  3
b. y  2 x  3
c. y  x  6
d. x  y  7
e. 2 x  3 y  1
f. y  4 x  7
g. x  y  7
h. y  x
i. y   x
6
3.
4.
j. 4 x  5 y  2
Check your work with the graphing calculator
Hand in your work. NEATNESS COUNTS! Only a PERFECT PAPER will receive a 20/20
Algebra 1
Lesson- Parallel and Perpendicular Lines
Name:____________________________________
Date:_____________________________________
Objective: To discover the properties among parallel and perpendicular line.
Do Now- Answer the following two questions using complete thoughts:
1.
What is the slope formula?
2.
What is a line?
Ex 1: Find the slope of:
a. Line AB if A(2,2) and B(4,6)
b. Line CD if C(6,4) and D(7,6)
c. Graph the lines from a and b on the same graph
Ex2: Find the slope of:
a. Line AB if A(2,2) and B(4,5)
b. Line BC if B(4,5) and C(7,3)
c. Graph the lines from a and b on the same graph.
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d. What type of intersection is formed?
e. Describe the relationship between the results from
parts a and b.
Define: Parallel-
What do we know about the slopes of 2 parallel lines?
Define: Perpendicular:
What do we know about the slopes of 2 parallel lines?
Ex. 3: In trapezoid ABCD, AB is parallel to DC. The vertices are A(1,4), B(3,5), C(k,3), D(1,1).
a. Find the slope of AB.
b. Express the slope of DC in terms of k.
c. Write an equation that can be used to solve for k.
d. Find the value of k.
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Algebra 1
Lesson- Writing Linear Equations
Name:____________________________________
Date:_____________________________________
Objective:
To be able to write the equation of a line given the slope and a point on the line
To be able to write the equation of a line given two points
Examples:
a) Find a slope-intercept equation for the line with slope 2 that contains (0,5).
b) Find a slope intercept equation for the line with slope 4 that contains (7,0).
Examples:
Write the equation of the line given the following information
1.
(4,-3), m = -1
2.
(-5,-6), m= 2
3.
(3,5), m = -2
(- 7,2), m = 3
4.
9
5.
(6,-2), m= -3
6.
(5,-2), m= 2
7.
(0,9), m = -2
8.
(2,1), m= 3
Writing the equation of the line connecting 2 points:
What is the formula for finding the slope of the line connecting 2 points?
Procedure
Example: Write the equation of the line passing through (1,4) and (5, 2)
Write the equation of the line passing through the given points.
1. (0,0) and (2,1)
2. (1,2) and (3,4)
3. (-1,2) and (-3,-5)
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4. (1,1) and (5, 4)
5. (-1,3) and (4,3)
6. (2,2) and (-3,7)
7. (4,5) and (9.8)
8. (15,2) and (18,19)
 1   3

9.  ,2  &  ,1
 2  2

What is the relationship between the slopes of two parallel lines?
What is the relationship between the slopes of two perpendicular lines?
Write an equation of a line that is:
a.
parallel to the line y  3x  9 and has a y intercept of 3.
b.
parallel to the line x  2 y  7 and has a y intercept of -6
c.
parallel to the line 3 x  3 y  12 and passes through the point (2,4)
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d.
perpendicular to the line y  2 x  4 and has a y intercept of -12
e.
perpendicular to the line 3x  4 y  12 and passes through (1,2)
Algebra 1
HW- Writing the equation of a line
Name:____________________________________
Date:_____________________________________
Write the equation of the line given the following:
1. m=2; (1,4)
2. m=2; (-3,4)
3. m= -3; (-2, -1)
4. m=1/2; (4,2)
5. m= -3/4; (0,0)
6. m= -5/3; (-3,0)
7. (1,4); (3,8)
8. (3,1); (9,7)
9. (1,2); (10,14)
10. (0,-1); (6,8)
11. (-2,-5); (-1,-2)
12. (0,0); (-3,5)
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13. Write the equation of the line that is:
a.
parallel to the line y  2 x  4 and has a y intercept of 7.
b.
parallel to the line y  3x  6 and has a y intercept of -2
c.
parallel to the line 2 x  3 y  12 and passes through the origin
d.
perpendicular to the line y  3x  2 and has a y intercept of 2
e.
perpendicular to the line 3x  4 y  18 and passes through the origin
Algebra 1
Lesson: Solving Linear Systems Graphically
Name:____________________________________
Date:_____________________________________
Objective:
To be able to solve linear systems of equations using graphs
Do Now:
Graph the following function.
y  3x  1
__________________________________________________________________________________________
Solving linear systems:
Solving Systems of Equations Graphically:
Graph both lines and determine the point at which the two lines intersect.
Example: Solve the following system graphically
3x  y  13
x  6 y  7
y
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Practice Problems
Solve each of the following systems of equations graphically. Note: You may need to scale the graph.
1.
y  2x
2.
y  3x  3
x y  4
x y 0
y
y
x
3.
4x  y  9
x
4.
2 x  y  12
y
x3
y4
y
14
5.
1
x 3
3
2x y  8
y
6.
y
y  - 3x
5y - 2x  10
y
x
x
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Algebra 1
Lesson: Solving systems of equations algebraically
Name:____________________________________
Date:_____________________________________
Objective:
To be able to solve systems of equations using the addition method and the
substitution method
y
Do Now: Find the graphical solution of the following:
2x  y  3
4x  3y  1
x
Addition Method:
Examples:
Solve for x and y:
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1.
x  y  12
x y  4
2.
Practice Problems:
Solve each of the following using the addition method:
x  2y  8
4 x  y  10
3.
4.
2 x  3 y  12
x  2y  4
3a  7  7b
4a  3b  22
5.
4a  6b  15
6a  4b  10
__________________________________________________________________________________________
Substitution Method:
Example:
Solve for x and y:
a  2b
6.
5a  3b  13
Solve each of the following using the substitution method:
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7.
9.
yx
x  y  14
sr 0
rs 6
Algebra 1
Lesson- Using the graphing calculator in
Coordinate Geometry
y  3x
8.
10.
1
1
x  y  11
3
2
x  y  300
0.25 x  0.75 y  195
Name:____________________________________
Date:_____________________________________
Objective: To be able to use the graphing calculator to:
 Graph lines using the table method
 Write the equation of a line given 2 points
 Find solutions of linear systems graphically
__________________________________________________________________________________________
Do Now: Write the equation of the line passing through (1,2) and (3,6)
__________________________________________________________________________________________
Resetting a Graphing Calculator
__________________________________________________________________________________________
Graphing lines using the table method on the graphing calculator
y
1
y  x2
Example 1:
2
x
__________________________________________________________________________________________
Writing the equation of a line given 2 points on the graphing calculator
(2,3); (5,9)
Example 2:
18
__________________________________________________________________________________________
Finding solutions of linear systems graphically on the graphing calculator
y  x  2; y   x  4
Example 3:
y
x
Algebra 1
Wkst- Using the graphing calculator in Coordinate
Geometry
Name:____________________________________
Date:_____________________________________
Answer each of the following neatly and completely
Use the graphing calculator to write the equation of a line passing through:
1. (0,0) & (6,9)
2. (-1,3) & (2,4)
3. (5,4) & (6,2)
5. (0.23, 0.48) & (1,2)
6. (3,3.14) & (4, 5.99)
7. (-1,-2) & (420, 17)
4. (-1,-2) & (-2,3)
8. (32.7, 21) & (1,375)
Use the graphing calculator to come up with a table of values for each of the following given (3  x  3)
37
x4
9. y 
10. y  3x  2
11. y  2 x  73.5
12. 2 x  y
21
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Use the graphing calculator to find the point of intersection between each pair of lines (if any) round any
decimals to three places.
2
y  x4
yx
yx
x  12  y
3
13.
14.
15.
16.
y  x
y  x  12
y  4.2 x  17.69
3
y
x4
2
Algebra 1
Lesson: Solving verbal systems in 2 variables
Name:____________________________________
Date:_____________________________________
Objective:
To be able to solve word problems using systems of equations and/or inequalities.
Do Now: Find the solution of the following:
y  3x
y  x  18
Solving word problems using multiple equations:
Example:
The sum of two numbers is 10. Three times the larger decreased by twice the smaller is 15. Find
the numbers.
Process:
Solution:
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Practice Problems:
1.
One number is 15 larger than another. The sum of twice the larger and three times the smaller is 180.
Find the numbers.
2.
Ms. Jordan bought 2 pounds of veal and 3 pounds of pork, for which she paid $20.00. Mr. Kermani,
paying the same prices, paid $11.25 for 1 pound of veal and 2 pounds of pork. Find the price of a
pound of veal and a pound of pork.
3.
The perimeter of a rectangle is 50 cm. The length is 9 cm more than the width. Find the length and
width of the rectangle.
4.
One year, Chris Duncan and his wife Jamie together earned $47,000. If Chris earned $4,000 more than
Jamie earned that year, how much did each earn?
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5.
In an isosceles triangle, each base angle measures 30 degrees more than the vertex angle. Find the
degree measures of the three angles of the triangle.
Algebra 1
Lesson: Solving Inequality Systems Graphically
Name:____________________________________
Date:_____________________________________
Objective:
To be able to solve linear systems of inequalities using graphs
Do Now:
Graph the following function.
y
1
x 1
3
_________________________________________________________________________________________
Solving linear systems:
y
Example: Solve the following system graphically
3x  y  3
 x  6 y  6
x
Practice Problems
Solve each of the following systems of inequalities graphically.
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1.
y 1
2.
y  2
y
y  2x  3
y  x
y
x
3.
x
x  y  2
4.
x y  2
y
2x  3y  6
x y4 0
y
x
x
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