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Geometry B Name:______________________ Date: ___________
Chapter 3: Parallel and Perpendicular Lines
Section 3.5: Slope of Lines
Are you ready? (This should be completed for homework.)
Find the value of m.
1. 2.
3. 4.
Why learn this?____________________________________________
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Objectives of Lesson: ________________________________________
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The slope_________________________________________________
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Slope of a Line
Definition Example
2
Example 1: Finding the Slope of a Line
Use the slope formula to determine the slope of each line: AB, AC, AD and
CD
Remember_________________________________________________
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Example 2: Finding the Slope of a Line
Use the slope formula to determine the slope of JK through J(3, 1) and
K(2, –1).
Summary: Slope of a Line
Positive Slope Negative Slope Zero Slope Undefined Slope
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One interpretation__________________________________________
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Example 3: Transportation Application
Justin is driving from home to his college dormitory. At 4:00 p.m., he is 260
miles from home. At 7:00 p.m., he is 455 miles from home. Graph the line
that represents Justin’s distance from home at a given time. Find and
interpret the slope of the line.
Example 3: Application
Tony is driving from Dallas, Texas, to Atlanta, Georgia. At 3:00 P.M., he is
180 miles from Dallas. At 5:30 P.M., he is 330 miles from Dallas. Graph the
line that represents Tony’s distance from Dallas at a given time. Find and
interpret the slope of the line.
Example 4: What if…? Use the graph above to estimate how far Tony will
have traveled by 6:30 P.M. if his average speed stays the same.
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Slopes of Parallel and Perpendicular Lines
Parallel Lines Theorem
Perpendicular Lines Theorem
If a line __________________________________________________
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Caution: __________________________________________________
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Example 5: Determining Whether Lines Are Parallel, Perpendicular, or
Neither
Graph each pair of lines. Use their slopes to determine whether they are
parallel, perpendicular, or neither.
UV and XY for U(0, 2), V(–1, –1), X(3, 1), and Y(–3, 3)
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Example 6: Determining Whether Lines Are Parallel, Perpendicular, or
Neither
Graph each pair of lines. Use their slopes to determine whether they are
parallel, perpendicular, or neither.
CD and EF for C(–1, –3), D(1, 1), E(–1, 1), and F(0, 3)
Example 7: Determining Whether Lines Are Parallel, Perpendicular, or
Neither
Graph each pair of lines. Use their slopes to determine whether they are
parallel, perpendicular, or neither.
GH and IJ for G(–3, –2), H(1, 2), I(–2, 4), and J(2, –4)
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Example 8: Determining Whether Lines Are Parallel, Perpendicular, or
Neither
Graph each pair of lines. Use their slopes to determine whether they are
parallel, perpendicular, or neither.
WX and YZ for W(3, 1), X(3, –2), Y(–2, 3), and Z(4, 3)
Example 9: Determining Whether Lines Are Parallel, Perpendicular, or
Neither
Graph each pair of lines. Use their slopes to determine whether they are
parallel, perpendicular, or neither.
KL and MN for K(–4, 4), L(–2, –3), M(3, 1), and N(–5, –1)
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Example 10: Determining Whether Lines Are Parallel, Perpendicular, or
Neither
Graph each pair of lines. Use their slopes to determine whether they are
parallel, perpendicular, or neither.
BC and DE for B(1, 1), C(3, 5), D(–2, –6), and E(3, 4)
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