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3-6

3-6. Lines in the Coordinate Plane. Warm Up. Lesson Presentation. Lesson Quiz. Holt Geometry. Warm Up Substitute the given values of m, x, and y into the equation y = mx + b and solve for b . 1. m = 2, x = 3, and y = 0 Solve each equation for y . 3. y – 6 x = 9.

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3-6

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  1. 3-6 Lines in the Coordinate Plane Warm Up Lesson Presentation Lesson Quiz Holt Geometry

  2. Warm Up Substitute the given values of m, x, and y into the equation y = mx + b and solve for b. 1. m = 2, x = 3, and y = 0 Solve each equation for y. 3. y –6x = 9 b = –6 2.m = –1, x = 5, and y = –4 b = 1 y = 6x + 9 4. 4x –2y = 8 y = 2x – 4

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

  4. Vocabulary point-slope form slope-intercept form

  5. Find the slope and y-intercept of each line and then graph each line.

  6. y = 2x + 5

  7. 1 2 y = - x – 7

  8. y = 3x

  9. y = 3

  10. y = - 4x + 3

  11. x = 4

  12. x – 2y = 6

  13. 4x + 3y = -3

  14. x – y = 2

  15. 5x + 3y = 0

  16. x = 6

  17. - x + 5y + 5 = 0

  18. 0 = -2x – y - 3

  19. -3x = -5 – y

  20. Example 1A: Writing Equations In Lines Write the equation of each line. the line with slope 5 and a y-intercept of -2

  21. Example 1A: Writing Equations In Lines Write the equation of each line. the line with slope 0 and a y-intercept of 3

  22. Example 1A: Writing Equations In Lines Write the equation of each line. the line with slope 6 through (3, –4)

  23. Example 1A: Writing Equations In Lines Write the equation of each line. the line with slope -2 through (-2, 4)

  24. Example 1B: Writing Equations In Lines Write the equation of each line in the given form. the line through (–1, 0) and (1, 2)

  25. Check It Out! Example 1a Write the equation of each line in the given form. the line with slope 0 through (4, 6)

  26. Check It Out! Example 1b Write the equation of each line in the given form. the line through (–3, 2) and (1, 2)

  27. Check It Out! Example 1b Write the equation of each line in the given form. the line through (–7, 9) and (-4, -2)

  28. 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.

  29. Example 3A: Classifying Pairs of Lines Determine whether the lines are parallel, intersect, or coincide. y = 3x + 7, y = –3x – 4

  30. Example 3B: Classifying Pairs of Lines Determine whether the lines are parallel, intersect, or coincide.

  31. Example 3C: Classifying Pairs of Lines Determine whether the lines are parallel, intersect, or coincide. 2y – 4x = 16, y – 10 = 2(x - 1)

  32. Check It Out! Example 3 3x + 5y = 2 and 3x + 6 = -5y

  33. 2. the line through (5, –1) with slope in point-slope form. y + 1= (x – 5) 2 5 Lesson Quiz: Part I Write the equation of each line in the given form. Then graph each line. 1. the line through (-1, 3) and (3, -5) in slope-intercept form. y = –2x + 1

  34. 1 2 Lesson Quiz: Part II Determine whether the lines are parallel, intersect, or coincide. 3. y – 3 = – x, y – 5 = 2(x+ 3) intersect 4.2y = 4x + 12, 4x – 2y = 8 parallel

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