Name____________________________________ Date _________________ Block ____
Slope Investigation
Signs of Slopes
Parallel and Perpendicular Lines
Materials needed: PENCIL, RULER
The following investigations are designed to do individually and then compare
results with your desk buddy. You MUST use a ruler and a pencil. Although we
will review the answers as a class, this packet will be graded for thoroughness of
answers and accuracy and neatness of all drawings. If the packet is not
completed in class, it is homework.
1
Investigation I
Follow the steps below to graph lines and explore their slopes.
1.
Label your first graph Slopes of Lines #1 and your second graph Slopes of Lines #2.
2.
Plot the ordered pairs (-5, 1) and (-1, 5) on Slopes of Lines #1. Label them A and B.
Draw a line through your points. Be sure to hold your ruler steady and make a very
thin, straight line.
3.
Plot another set of ordered pairs (-1, -3) and (6, 0) on Slopes of Lines #1. Label these
points C and D. Draw this line.
4.
Plot the ordered pairs (-5, 1) and (-1, -5) on Slopes of Lines #2. Label them E and F.
Draw a line through your points.
5.
Plot another set of ordered pairs (3, 5) and (9, 0) on Slopes of Lines #2. Label these
points G and H. Draw this line.
2
Using your ordered pairs (don’t count up/down and over), show your work using the slope
formula to find the slope of each line.
Slopes of Lines #1
SHOW WORK FOR SLOPE HERE
Slope of AB = _________________
Slope of CD = _________________
Slopes of Lines #2
Slope of EF = _________________
Slope of GH = _________________
What do you notice about the slopes of lines AB and CD (hint: look at the signs)?
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What do the graphs of lines AB and CD have in common?
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Compare your results with your desk buddy. Is there a common result? Explain.
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What do you notice about the slopes of lines EF and GH (hint: look at the signs)?
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What do the graphs of lines EF and GH have in common?
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Compare your results with your desk buddy. Is there a common result? Explain.
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State your conclusion about the relationship between the sign of the slope and the graph of
the line. BE SPECIFIC!
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3
Investigation II
Follow the steps below to draw pairs of parallel lines on your graph paper.
1.
Label your first graph Parallel Lines #1 and your second graph Parallel Lines #2.
2.
Plot the ordered pairs (-7, 2) and (-3, 5) on Parallel Lines #1. Label them A and B. Draw
a line through your points.
3.
Plot another set of ordered pairs (-2, -3) and (2, 0) on Parallel Lines #1. Label these
points C and D. Draw this line.
4.
Plot the ordered pairs (-3, 6) and (7, 0) on Parallel Lines #2. Label them L and M. Draw
a line through your points.
5.
Plot another set of ordered pairs (-5, 0) and (0, -3). Label these points N and O. Draw
this line.
4
Using your ordered pairs (don’t count up/down and over), show your work using the slope
formula to find the slope of each line.
Parallel Lines #1
SHOW WORK FOR SLOPE HERE
Slope of AB = _________________
Slope of CD = _________________
Parallel Lines #2
Slope of LM = _________________
Slope of NO = _________________
What do you notice about the slopes of the parallel lines?
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Compare your results with your desk buddy. Is there a common result? Explain.
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State your conclusion about the relationship of slopes of lines that are parallel referring to the
calculations that you made to determine the slopes of the lines.
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5
Investigation III
Follow the steps below to draw pairs of lines, which are perpendicular.
1.
Label your graphs Perpendicular Lines #1 and Perpendicular Lines #2.
2.
Plot the points (-1, 8), (2, 3), and (7, 6) on Perpendicular Lines #1. Label these points X,
Y and Z.
4.
Take your ruler and draw lines XY and YZ.
5.
Plot the points (-6, -4), (-1, -3), and (0, -8) on Perpendicular Lines #2. Label these points
L, M and N.
4.
Take your ruler and draw lines LM and MN.
6
Find the slopes, using the slope formula, not counting up/down and over, of XY, YZ, and LM
and MN.
Perpendicular Lines
SHOW WORK FOR SLOPE HERE
Slope of XY: _________
Slope of YZ: _________
Slope of LM: _________
Slope of MN: _________
What do you notice about the slopes of the perpendicular lines?
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What do you notice about the product of the slopes?
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Compare your results with your desk buddy. Is there a common result? Explain.
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__________________________________________________________________
State your conclusion about relationship of the slopes of lines that are perpendicular referring
to the calculations that you made to determine the slopes of the lines:
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7
Summarize what you have learned from this investigation and from yesterday’s notes:
1. What will the graph of a line with a positive slope look like? Be specific and sketch an
example.
2. What will the graph of a line with a negative slope look like? Be specific and sketch
an example.
3. What will the graph of a line with a 0 slope look like? Be specific and sketch an
example.
4. What will the graph of a line with an undefined slope look like? Be specific and sketch
an example.
5. Finish this sentence: The slopes of two lines that are parallel will be…
6. Finish this sentence: If the slopes of two lines have the same value, you can conclude
that they are….
7. Finish this sentence: The slopes of two lines that are perpendicular will be…
8. Finish this sentence: If the slopes of two lines are opposite and reciprocals, you can
conclude that they are…
8