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Chapter 3

Chapter 3 . 3-6 Lines in the coordinate plane. Objectives. Graph lines and write their equations in slope-intercept and point-slope form. Classify lines as parallel, intersecting, or coinciding. Equation of a line .

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Chapter 3

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  1. Chapter 3 3-6 Lines in the coordinate plane

  2. Objectives Graph lines and write their equations in slope-intercept and point-slope form. Classify lines as parallel, intersecting, or coinciding.

  3. Equation of a line • The equation of a line can be written in many different forms. The point-slope and slope-intercept forms of a line are equivalent. Because the slope of a vertical line is undefined, these forms cannot be used to write the equation of a vertical line.

  4. Forms of the equation of a line

  5. Example#1 • Write the equation of each line in the given form. • the line with slope 6 through (3, –4) in point-slope form.

  6. Example#2 • Write the equation of each line in the given form. • the line through (–1, 0) and (1, 2) in slope-intercept form.

  7. Example#3 • Write the equation of each line in the given form. • the line with the x-intercept 3 and y-intercept –5 in point slope form.

  8. Student guided practice • Do problems 2-4 in your book page 194

  9. run 2 rise 1 (0, 1) Graphing Equations of the line • Graph each line.

  10. rise –2 (–4, 3) run 1 Example#4 • Graph each line. • y – 3 = –2(x + 4)

  11. (0, –3) Example#5 • Graph each line. • y = –3

  12. Example#6 • Graph each line. • x= 4

  13. Student guided practice • Do problems 5-7

  14. Equations of lines • A system of two linear equations in two variables represents two lines. The lines can be parallel, intersecting, or coinciding. Lines that coincide are the same line, but the equations may be written in different forms.

  15. Pair of lines

  16. Example#7 • Determine whether the lines are parallel, intersect, or coincide. • y = 3x + 7, y = –3x – 4 • The lines have different slopes, so they intersect.

  17. Example#8 • Determine whether the lines are parallel, intersect, or coincide. Both lines have a slope of -1/3, and the y-intercepts are different. So the lines are parallel.

  18. Example#9 • Determine whether the lines are parallel, intersect, or coincide. • 2y – 4x = 16, y – 10 = 2(x - 1) • Both lines have a slope of 2 and a y-intercept of 8, so they coincide.

  19. Student guided practice • Do problems 8-11 in your book page 194

  20. Problem solving application • Erica is trying to decide between two car rental plans. For how many miles will the plans cost the same?

  21. Lesson Quiz • Identify each of the following: • 1. a pair of parallel segments • 2. a pair of skew segments

  22. Lesson Quiz • State the theorem or postulate that is related to the measures of the angles in each pair. Then find the unknown angle measures. • 3. m3 = (50x + 20)°, m4= (100x – 80)° • 4. m3 = (45x + 30)°, m5 = (25x + 10)°

  23. Lesson Quiz • Use the theorems and given information to prove p || r. • 5. m2 = (5x + 20)°, m 7 = (7x + 8)°, and x = 6

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