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Mastering Linear Equations: Graphing, Classification & Problem-Solving

Learn to write and classify lines using slope-intercept & point-slope forms, and solve real-life problems involving linear equations. Practice graphing lines and determining if they are parallel, intersecting, or coinciding. Apply your knowledge to practical situations.

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Mastering Linear Equations: Graphing, Classification & Problem-Solving

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

  2. Vocabulary point-slope form slope-intercept form

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

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

  5. Example 1C Write the equation of each line in the given form. the line with slope 0 through (4, 6) in slope-intercept form

  6. Example 2A Graph each line. y = 2x – 3

  7. Example 2B: Graphing Lines Graph each line. y – 3 = –2(x + 4)

  8. Example 2C Graph each line. y = –3

  9. 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.

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

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

  12. Example 4: Problem-Solving Application Erica is trying to decide between two car rental plans. For how many miles will the plans cost the same?

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