example 1
DESCRIPTION
Find the slope of line a and line d. – 1. =. =. =. =. 2. 4. =. =. =. – 2. 0. y 2 – y 1. y 2 – y 1. 4 – 0. 4 – 2. x 2 – x 1. x 2 – x 1. 6 – 8. 6 – 6. EXAMPLE 1. Find slopes of lines in a coordinate plane. SOLUTION. Slope of line a : m. Slope of line d : m. - PowerPoint PPT PresentationTRANSCRIPT
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EXAMPLE 1 Find slopes of lines in a coordinate plane
Find the slope of line a and line d.
SOLUTION
Slope of line a: m = – 1
Slope of line d: m =4 – 0 6 – 6
= 4 0
which is undefined.
y2 – y1 x2 – x1
= = 4 – 2 6 – 8
= 2– 2
y2 – y1 x2 – x1
=
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GUIDED PRACTICE for Example 1
Use the graph in Example 1. Find the slope of the line.
1. Line b
2ANSWER
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GUIDED PRACTICE for Example 1
Use the graph in Example 1. Find the slope of the line.
2. Line c
0ANSWER
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EXAMPLE 2 Identify parallel lines
Find the slope of each line. Which lines are parallel?
SOLUTION
Find the slope of k1 through (– 2, 4) and (– 3, 0).
= – 4 – 1 = 4
m21 – 5 3 – 4
= = 4
Find the slope of k2 through (4, 5) and (1, 3).
=– 4 – 1
m1 =0 – 4
– 3 – (– 2 )
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EXAMPLE 2 Identify parallel lines
m3– 2 – 3 5 – 6
= =– 5 – 1
= 5
Find the slope of k3 through (6, 3) and (5, – 2).
Compare the slopes. Because k1 and k2 have the same slope, they are parallel. The slope of k3 is different, so k3 is not parallel to the other lines.
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GUIDED PRACTICE for Example 2
3. Line m passes through (–1, 3) and (4, 1). Line t passes through (–2, –1) and (3, – 3). Are the two lines parallel? Explain how you know.
Yes; they have the same slope.
ANSWER
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EXAMPLE 3 Draw a perpendicular line
SOLUTION
Line h passes through (3, 0) and (7, 6). Graph the line perpendicular to h that passes through the point (2, 5).
= 64
= 32
m1 = 6 – 0 7 – 3
STEP 1
Find the slope m1 of line h through (3, 0) and (7, 6).
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EXAMPLE 3 Draw a perpendicular line
STEP 2
Find the slope m2 of a line perpendicular to h. Use the fact that the product of the slopes of two perpendicular lines is –1.
m2 =32
– 1
m2 = – 2 3
Slopes of perpendicular lines
23
Multiply each side by
STEP 3
Use the rise and run to graph the line.
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GUIDED PRACTICE for Examples 3 and 4
4. Line n passes through (0, 2) and (6, 5). Line m passes through (2, 4) and (4, 0). Is n m? Explain.
ANSWER Yes; the product of their slopes is – 1.
5. In Example 4, which parachute is in the air for the longest time? Explain.
SAMPLE ANSWER
Parachute C. It was in the air approximately 1.25 minutes longer than either a or b.
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• http://www.classzone.com/cz/books/geometry_2007_na/resources/applications/animations/geom07_ch03_pg174.html
• http://www.classzone.com/cz/books/geometry_2007_na/resources/applications/animations/explore_learning/chapter_3/dswmedia/Alg1_4_6_Slope_I.html