Slopes of of Parallel and and Perpendicular Lines Lines Holt Algebra 1

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1 5-8 Slopes of of Parallel and and Lines Warm Up Lesson Presentation Lesson Quiz

2 Bell Quiz 5-8 Find the reciprocal pt 1 pt 1 pt 3. 2 pts 2 pts 2 pts Find the slope of the line that passes through each pair of points. 4. (2, 2) and ( 1, 3) 10 pts 5. (3, 4) and (4, 6) possible 6. (5, 1) and (0, 0) 1 pt for putting your name on your paper

3 Questions on 5-7

4 Questions on 5-7

5 Objectives Identify and graph parallel and perpendicular lines. Write equations to describe lines parallel or perpendicular to a given line.

6 parallel lines Vocabulary perpendicular lines

7 To sell at a particular farmers market for a year, there is a $100 membership fee. Then you pay $3 for each hour that you sell at the market. However, if you were a member the previous year, the membership fee is reduced to $50. The red line shows the total cost if you are a new member. The blue line shows the total cost if you are a returning member.

8 These two lines are parallel. Parallel lines are lines in the same plane that have no points in common. In other words, they do not intersect.

10 Example 1A: Identifying Parallel Lines Identify which lines are parallel.

11 Example 1B: Identifying Parallel Lines Identify which lines are parallel.

12 Example 1B Continued The lines described by y = 2x 3 and y + 1 = 3(x 3) are not parallel with any of the lines. The lines described by y = 2x 3 and represent parallel lines. They each have the slope. y + 1 = 3(x 3)

13 Check It Out! Example 1a Identify which lines are parallel. y = 2x + 2; y = 2x + 1; y = 4; x = 1 y = 2x + 2 y = 2x + 1 y = 4 x = 1

14 Check It Out! Example 1b Identify which lines are parallel.

15 Check It Out! Example 1b Continued The lines described by 3x + 4y = 32 and y = + 8 have the same slope, but they are not parallel lines. They are the same line. 3x + 4y = 32 y = 3x The lines described by y = 3x and y 1 = 3(x + 2) represent parallel lines. They each have slope 3. y 1 = 3(x + 2)

16 Example 2: Geometry Application Show that JKLM is a parallelogram. Use the ordered pairs and the slope formula to find the slopes of MJ and KL.

17 Check It Out! Example 2 Show that the points A(0, 2), B(4, 2), C(1, 3), D( 3, 3) are the vertices of a parallelogram. A(0, 2) B(4, 2) D( 3, 3) C(1, 3)

18 Perpendicular lines are lines that intersect to form right angles (90 ).

19 Helpful Hint If you know the slope of a line, the slope of a perpendicular line will be the "opposite reciprocal.

21 Example 3: Identifying Identify which lines are perpendicular: y = 3; x = 2; y = 3x;. x = 2 y = 3 y =3x

22 Example 3 Continued Identify which lines are perpendicular: y = 3; x = 2; y = 3x;. x = 2 y = 3 y =3x

23 Check It Out! Example 3 Identify which lines are perpendicular: y = 4; y 6 = 5(x + 4); x = 3; y = x = 3 y = 4 y 6 = 5(x + 4)

24 Check It Out! Example 3 Continued Identify which lines are perpendicular: y = 4; y 6 = 5(x + 4); x = 3; y = x = 3 y = 4 y 6 = 5(x + 4)

25 Example 4A: Writing Equations of Parallel and Write an equation in slope-intercept form for the line that passes through (4, 10) and is parallel to the line described by y = 3x + 8. Step 1 Find the slope of the line. Step 2 Write the equation in point-slope form. Step 3 Write the equation in slope-intercept form

26 Example 4B: Writing Equations of Parallel and Write an equation in slope-intercept form for the line that passes through (2, 1) and is perpendicular to the line described by y = 2x 5.

27 Check It Out! Example 4a Write an equation in slope-intercept form for the line that passes through (5, 7) and is parallel to the line described by y = x 6.

28 Check It Out! Example 4b Write an equation in slope-intercept form for the line that passes through ( 5, 3) and is perpendicular to the line described by y = 5x.

29 HOMEWORK Sec 5-8 (Pg 353) 1-8, 9, 12, 15, 17, 18, 20, 22, 25, 28, 31, 34, 37, 40, 43, 60, 61, 63, 64

Warm-Up. Complete the second homework worksheet (the one you didn t do yesterday). Please begin working on FBF010 and FBF011.

Warm-Up. Complete the second homework worksheet (the one you didn t do yesterday). Please begin working on FBF010 and FBF011. Warm-Up Complete the second homework worksheet (the one you didn t do yesterday). Please begin working on FBF010 and FBF011. You have 20 minutes at the beginning of class to work on these three tasks.