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Numbers and Their Application to Math and Science

Homework for Numbers Lesson 12

  1. Aunt Ethel hands you $15 in quarters (q) and dimes (d). Name five ordered pairs (q,d) representing the change she might have given you. Graph the points. What relation do you observe?

     

  2. What are the slopes of the line containing points (0,2) and (9,5) and the line with points (-1,4) and (5,8)? Which line is steeper?

     

  3. Prove that "If two lines are parallel to the same line, then they are parallel to each other."

     

  4. If the slope of a line is -3/4, what is the slope of a perpendicular line to it?

     

    For problems 5 - 8, classify the following lines as vertical, horizontal, or oblique (neither):

  5. x + y = 2

     

  6. 2x = 6

     

  7. 3x - 2y = 1

     

  8. y = 17 - 5

     

  9. Graph: y = 3x + 2.

     

  10. Graph: x + 4y = 4

     

  11. Determine if the following system of equations is inconsistent, independent, or dependent:

    2x - 3y = 5
    10x - 15y = 25.

  12. Determine if the following system of equations is inconsistent, independent, or dependent:

    6x + 4y = 3
      x - 1.5y = 4.

     

  13. Find a line perpendicular to the given line: 4x - y = 3.

     

  14. Graph the equation y = x2 - 3.     Is it a relation or a function?

     

  15. Graph the equation x2 + y2 = 4. Is it a relation or a function? (If doing by calculator, solve for y. Enter into calculator both branches for y due to ± the square root.)

     

  16. Graph the function y = x2 + 5x + 6.     Find the domain and range.

     

  17. Graph the function y = x2 - 4x + 4.     Find the domain and range.

     

  18. Solve the equation for x.   5x2 + 8x - 6 = 3.

     

  19. Determine if the equation has real solutions. 4x2 - 13x + 11 = 0.

     

  20. Solve the equation, y = x2 - 4x + 5, when y = 0. What does this infer about the graph of the function?

     

  21. Read sections 3.6 and 3.7 in your geometry textbook and do problem 9 in both.
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