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3.5 – Write and Graph Equations of Lines

Learn to write and graph linear equations, including slope-intercept and standard form. Explore examples with parallel and perpendicular lines. Understand the meanings of slope and y-intercept in context. Solve real-world problems involving linear equations. Improve your skills in algebra with practical exercises.

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3.5 – Write and Graph Equations of Lines

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  1. 3.5 – Write and Graph Equations of Lines Linear equations may be written in different forms. The general form of a linear equation in slope-intercept form y = mx+b, where m is the slope and b is the y-intercept.

  2. 3.5 – Write and Graph Equations of Lines Example 1: Write an equation of the line in slope-intercept form.

  3. 3.5 – Write and Graph Equations of Lines Example 2: Write an equation of the line in slope-intercept form.

  4. 3.5 – Write and Graph Equations of Lines Example 3: Write an equation of the line passing through the point (-1, 1) that is parallel to the line with the equation y = 2x – 3.

  5. 3.5 – Write and Graph Equations of Lines Example 4: Write an equation of the line passing through the point (2, -3) that is parallel to the line with the equation y = 6x +4.

  6. 3.5 – Write and Graph Equations of Lines Example 5: Write an equation of the line passing through the point (2, 3) that is perpendicular to the line with the equation y = -2x + 2.

  7. 3.5 – Write and Graph Equations of Lines Example 6: Write an equation of the line passing through the point (3, -4) that is perpendicular to the line with the equation y = -1/2x - 1

  8. 3.5 – Write and Graph Equations of Lines Example 7: The graph models the total cost of joining a gym. Write an equation fo the line. Explain the meaning of the slope and the y-intercept of the line.

  9. 3.5 – Write and Graph Equations of Lines Example 8: The graph shows the cost of having cable television installed in your home. Write an equation of the line. Explain the meaning of the slope and y-intercept of the line.

  10. 3.5 – Write and Graph Equations of Lines Another form of a linear equation is standard form. In standard form, the equation is written as Ax + By = C, where A and B are not both zero.

  11. 3.5 – Write and Graph Equations of Lines Example 9: Graph 3x + 4y = 12

  12. 3.5 – Write and Graph Equations of Lines Example 10: Graph 2x – 3y = -12

  13. 3.5 – Write and Graph Equations of Lines Example 11: Graph 2(x-1) =-y

  14. 3.5 – Write and Graph Equations of Lines Example 11: Graph x – 3 = 0

  15. 3.5 – Write and Graph Equations of Lines Example 12: Graph y +3 = 2

  16. 3.5 – Write and Graph Equations of Lines Example 13: Graph 2y – 4 = 2x

  17. 3.5 – Write and Graph Equations of Lines Example 11: You can rent DVD’s at a local store for $4.00 each. An Internet company offers a flat fee of $15.00 per month for as many rentals as you want. How many DVD’s do you need to rent to make the online rental a better buy?

  18. 3.5 – Write and Graph Equations of Lines Example 12: One bank charges $1.50 for each use of its debit card. Another bank charges $10 per month for an unlimited number of debit card uses. How many times per month would you need to use your debit card to make the bank that charges a flat rate the better choice?

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