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Holt McDougal Geometry 3-5 Slopes of Lines 3-5 Slopes of Lines Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson.

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Presentation on theme: "Holt McDougal Geometry 3-5 Slopes of Lines 3-5 Slopes of Lines Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson."— Presentation transcript:

1 Holt McDougal Geometry 3-5 Slopes of Lines 3-5 Slopes of Lines Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz Holt McDougal Geometry

2 3-5 Slopes of Lines Warm Up Find the value of m. 1.2. 3.4. undefined0

3 Holt McDougal Geometry 3-5 Slopes of Lines Find the slope of a line. Use slopes to identify parallel and perpendicular lines. Objectives

4 Holt McDougal Geometry 3-5 Slopes of Lines rise run slope Vocabulary

5 Holt McDougal Geometry 3-5 Slopes of Lines The slope of a line in a coordinate plane is a number that describes the steepness of the line. Any two points on a line can be used to determine the slope.

6 Holt McDougal Geometry 3-5 Slopes of Lines

7 Holt McDougal Geometry 3-5 Slopes of Lines

8 Holt McDougal Geometry 3-5 Slopes of Lines Example 1A: Finding the Slope of a Line Use the slope formula to determine the slope of each line. Substitute (–2, 7) for (x 1, y 1 ) and (3, 7) for (x 2, y 2 ) in the slope formula and then simplify. AB

9 Holt McDougal Geometry 3-5 Slopes of Lines Example 1B: Finding the Slope of a Line Use the slope formula to determine the slope of each line. AC Substitute (–2, 7) for (x 1, y 1 ) and (4, 2) for (x 2, y 2 ) in the slope formula and then simplify.

10 Holt McDougal Geometry 3-5 Slopes of Lines The slope is undefined. Example 1C: Finding the Slope of a Line Use the slope formula to determine the slope of each line. AD Substitute (–2, 7) for (x 1, y 1 ) and (–2, 1) for (x 2, y 2 ) in the slope formula and then simplify.

11 Holt McDougal Geometry 3-5 Slopes of Lines A fraction with zero in the denominator is undefined because it is impossible to divide by zero. Remember!

12 Holt McDougal Geometry 3-5 Slopes of Lines Example 1D: Finding the Slope of a Line Use the slope formula to determine the slope of each line. CD Substitute (4, 2) for (x 1, y 1 ) and (–2, 1) for (x 2, y 2 ) in the slope formula and then simplify.

13 Holt McDougal Geometry 3-5 Slopes of Lines Check It Out! Example 1 Use the slope formula to determine the slope of JK through J(3, 1) and K(2, –1). Substitute (3, 1) for (x 1, y 1 ) and (2, –1) for (x 2, y 2 ) in the slope formula and then simplify.

14 Holt McDougal Geometry 3-5 Slopes of Lines

15 Holt McDougal Geometry 3-5 Slopes of Lines If a line has a slope of, then the slope of a perpendicular line is. The ratios and are called opposite reciprocals.

16 Holt McDougal Geometry 3-5 Slopes of Lines Four given points do not always determine two lines. Graph the lines to make sure the points are not collinear. Caution!

17 Holt McDougal Geometry 3-5 Slopes of Lines Example 3A: 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) The products of the slopes is –1, so the lines are perpendicular.

18 Holt McDougal Geometry 3-5 Slopes of Lines Example 3B: 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) The slopes are not the same, so the lines are not parallel. The product of the slopes is not –1, so the lines are not perpendicular.

19 Holt McDougal Geometry 3-5 Slopes of Lines Example 3C: 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) The lines have the same slope, so they are parallel.

20 Holt McDougal Geometry 3-5 Slopes of Lines Check It Out! Example 3a Graph each pair of lines. Use slopes to determine whether the lines are parallel, perpendicular, or neither. WX and YZ for W(3, 1), X(3, –2), Y(–2, 3), and Z(4, 3) Vertical and horizontal lines are perpendicular.

21 Holt McDougal Geometry 3-5 Slopes of Lines Check It Out! Example 3b Graph each pair of lines. Use slopes to determine whether the lines are parallel, perpendicular, or neither. KL and MN for K(–4, 4), L(–2, –3), M(3, 1), and N(–5, –1) The slopes are not the same, so the lines are not parallel. The product of the slopes is not –1, so the lines are not perpendicular.

22 Holt McDougal Geometry 3-5 Slopes of Lines Check It Out! Example 3c Graph each pair of lines. Use slopes to determine whether the lines are parallel, perpendicular, or neither. BC and DE for B(1, 1), C(3, 5), D(–2, –6), and E(3, 4) The lines have the same slope, so they are parallel.

23 Holt McDougal Geometry 3-5 Slopes of Lines Lesson Quiz 1. Use the slope formula to determine the slope of the line that passes through M(3, 7) and N(–3, 1). m = 1 Graph each pair of lines. Use slopes to determine whether they are parallel, perpendicular, or neither. 4, 4; parallel 2. AB and XY for A(–2, 5), B(–3, 1), X(0, –2), and Y(1, 2) 3. MN and ST for M(0, –2), N(4, –4), S(4, 1), and T(1, –5)


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