Name:_ I worked with:__ Comparing Two Lines Activity A.Identifying Slope and Y-Intercepts Identify the slope and y-intercept for each linear equation: i.Y=2x+3 a.Slope: 2 b.Y-intercept: 3 ii.Y=2x+6 a.Slope: 2 b.Y-intercept: 6 iii.Y=(-1/2)x+5 a.Slope: -1/2 b.Y-intercept: 5 B.Parallel Lines Example 1: Graph each linear equation on paper first, then use the simulation. For each, write down the slope and y-intercept of the line. After you have used the simulation, answer the questions on the worksheet. i.Y=4x+6 Slope = 4, y-intercept = 6 ii.Y=4x+3 Slope = 4, y-intercept = 3 Questions: What is similar about these two lines? What is different? The lines have the same slope, but different y-intercepts. Plot both lines on the same plane (first on paper, then with the simulation). What do you notice about the two lines (do they intersect, are they parallel)? They are parallel, and do not intersect. Example 2: Graph each linear equation on paper first, then use the simulation. For each, write down the slope and y-intercept of the line. After you have used the simulation, answer the questions on the worksheet. i.Y=-3x+3 Slope = -3, y-intercept = 3 ii.Y=-3x+4 Slope = -3, y-intercept = 4 Questions: What is similar about these two lines? What is different? The lines have the same slope, but different y-intercepts. Plot both lines on the same plane (first on paper, then with the simulation). What do you notice about the two lines (do they intersect, are they parallel)? They are parallel and do not intersect. C.Perpendicular Lines Example 1: Graph each linear equation on paper first, then use the simulation. For each, write down the slope and y-intercept of the line. After you have used the simulation, answer the questions on the worksheet. i.Y=2x+4 Slope = 2, y-intercept = 4 ii.Y=(-1/2)x+4 Slope = (-1/2), y-intercept = 4 Questions: What is similar about these two lines? What is different? The lines have the same y-intercept. Their slopes are different (the student may notice that they are opposite reciprocals of each other) Plot both lines on the same plane (first on paper, then with the simulation). What do you notice about the two lines (do they intersect, are they parallel)? They intersect. They might be perpendicular. Example 2: Graph each linear equation on paper first, then use the simulation. For each, write down the slope and y-intercept of the line. After you have used the simulation, answer the questions on the worksheet. i.Y=6x+7 Slope = 6, y-intercept = 7 ii.Y=(-1/6)x+7 Slope = (-1/6), y-intercept = 7 Questions: What is similar about these two lines? What is different? The lines have the same y-intercept, but different slopes. Plot both lines on the same plane (first on paper, then with the simulation). What do you notice about the two lines (do they intersect, are they parallel)? The lines intersect. They seem to be perpendicular. Example 3: Graph each linear equation on paper first, then use the simulation. For each, write down the slope and y-intercept of the line. After you have used the simulation, answer the questions on the worksheet. i.Y=6x+9 Slope = 6, y-intercept = 9 ii.Y=(-1/6)x+7 Slope = (-1/6), y-intercept = 7 Questions: What is similar about these two lines? What is different? In this case, the slopes and the y-intercepts are different. BUT the slopes are still opposite reciprocals of each other like they were in example 2. Plot both lines on the same plane (first on paper, then with the simulation). What do you notice about the two lines (do they intersect, are they parallel)? They STILL intersect, just at a different point to example 2. They are perpendicular. For each example, compare the slopes of the two lines. How are 2 and (-1/2) related? What about 6 and (-1/6)? What does this tell you about the slopes of perpendicular lines? (The student may not realize this until they answer this question). (-1/2) is the opposite reciprocal of 2, and (-1/6) is the opposite reciprocal of 6. The slopes of perpendicular lines are opposite reciprocals of each other. Think of two linear equations with the same slope and the same y-intercept: i.Y= 8x+9 ii.Y=8x+9 Graph them on the same plane (on paper, then on the simulation). What do you notice about this graph? They are the same line! They share infinitely many points.
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I worked with:__
Comparing Two Lines Activity
A. Identifying Slope and Y-Intercepts
Identify the slope and y-intercept for each linear equation:
i. Y=2x+3
a. Slope: 2
b. Y-intercept: 3
ii. Y=2x+6
a. Slope: 2
b. Y-intercept: 6
iii. Y=(-1/2)x+5
a. Slope: -1/2
b. Y-intercept: 5
B. Parallel Lines
Example 1: Graph each linear equation on paper first, then use the simulation. For each, write down the slope and y-intercept of the line. After you have used the simulation, answer the questions on the worksheet.
i. Y=4x+6
Slope = 4, y-intercept = 6
ii. Y=4x+3
Slope = 4, y-intercept = 3
Questions:
What is similar about these two lines? What is different?
The lines have the same slope, but different y-intercepts.
Plot both lines on the same plane (first on paper, then with the simulation). What do you notice about the two lines (do they intersect, are they parallel)?
They are parallel, and do not intersect.
Example 2: Graph each linear equation on paper first, then use the simulation. For each, write down the slope and y-intercept of the line. After you have used the simulation, answer the questions on the worksheet.
i. Y=-3x+3
Slope = -3, y-intercept = 3
ii. Y=-3x+4
Slope = -3, y-intercept = 4
Questions:
What is similar about these two lines? What is different?
The lines have the same slope, but different y-intercepts.
Plot both lines on the same plane (first on paper, then with the simulation). What do you notice about the two lines (do they intersect, are they parallel)?
They are parallel and do not intersect.
C. Perpendicular Lines
Example 1: Graph each linear equation on paper first, then use the simulation. For each, write down the slope and y-intercept of the line. After you have used the simulation, answer the questions on the worksheet.
i. Y=2x+4
Slope = 2, y-intercept = 4
ii. Y=(-1/2)x+4
Slope = (-1/2), y-intercept = 4
Questions:
What is similar about these two lines? What is different?
The lines have the same y-intercept. Their slopes are different (the student may notice that they are opposite reciprocals of each other)
Plot both lines on the same plane (first on paper, then with the simulation). What do you notice about the two lines (do they intersect, are they parallel)?
They intersect. They might be perpendicular.
Example 2: Graph each linear equation on paper first, then use the simulation. For each, write down the slope and y-intercept of the line. After you have used the simulation, answer the questions on the worksheet.
i. Y=6x+7
Slope = 6, y-intercept = 7
ii. Y=(-1/6)x+7
Slope = (-1/6), y-intercept = 7
Questions:
What is similar about these two lines? What is different?
The lines have the same y-intercept, but different slopes.
Plot both lines on the same plane (first on paper, then with the simulation). What do you notice about the two lines (do they intersect, are they parallel)?
The lines intersect. They seem to be perpendicular.
Example 3: Graph each linear equation on paper first, then use the simulation. For each, write down the slope and y-intercept of the line. After you have used the simulation, answer the questions on the worksheet.
i. Y=6x+9
Slope = 6, y-intercept = 9
ii. Y=(-1/6)x+7
Slope = (-1/6), y-intercept = 7
Questions:
What is similar about these two lines? What is different?
In this case, the slopes and the y-intercepts are different. BUT the slopes are still opposite reciprocals of each other like they were in example 2.
Plot both lines on the same plane (first on paper, then with the simulation). What do you notice about the two lines (do they intersect, are they parallel)?
They STILL intersect, just at a different point to example 2. They are perpendicular.
For each example, compare the slopes of the two lines. How are 2 and (-1/2) related? What about 6 and (-1/6)? What does this tell you about the slopes of perpendicular lines?
(The student may not realize this until they answer this question). (-1/2) is the opposite reciprocal of 2, and (-1/6) is the opposite reciprocal of 6. The slopes of perpendicular lines are opposite reciprocals of each other.
Think of two linear equations with the same slope and the same y-intercept:
i. Y= 8x+9
ii. Y=8x+9
Graph them on the same plane (on paper, then on the simulation). What do you notice about this graph?
They are the same line! They share infinitely many points.
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