41 Practice: Applications of Linear Equations(3.5 – 3.7) – — Intermediate Algebra

3.5 Constructing Linear Equations

For questions 1 to 12, write the slope-intercept form of each linear equation using the given point and slope.

1. and
2. and
3. and
4. and
5. and
6. and
7. and
8. and
9. and
10. and
11. and
12. and

For questions 13 to 24, write the general form of each linear equation using the given point and slope.

13. and
14. and
15. and
16. and
17. and
18. and
19. and
20. and
21. and
22. and
23. and
24. and

For questions 25 and 32, write the slope-intercept form of each linear equation using the given points.

25. and
26. and
27. and
28. and
29. and
30. and
31. and
32. and

For questions 33 to 40, write the general form of each linear equation using the given points.

33. and
34. and
35. and
36. and
37. and
38. and
39. and
40. and

<a class=”internal” href=”/intermediatealgebraberg/back-matter/answer-key-3-5/”>Answer Key 3.5

3.6 Perpendicular and Parallel Lines

For questions 1 to 6, find the slope of any line that would be parallel to each given line.

For questions 7 to 12, find the slope of any line that would be perpendicular to each given line.

For questions 13 to 18, write the slope-intercept form of the equation of each line using the given point and line.

13. (1, 4) and parallel to
14. (5, 2) and perpendicular to
15. (3, 4) and parallel to
16. (1, −1) and perpendicular to
17. (2, 3) and parallel to
18. (−1, 3) and perpendicular to

For questions 19 to 24, write the general form of the equation of each line using the given point and line.

19. (1, −5) and parallel to
20. (1, −2) and perpendicular to
21. (5, 2) and parallel to
22. (1, 3) and perpendicular to
23. (4, 2) and parallel to
24. (3, −5) and perpendicular to

For questions 25 to 36, write the equation of either the horizontal or the vertical line that runs through each point.

25. Horizontal line through (4, −3)
26. Vertical line through (−5, 2)
27. Vertical line through (−3,1)
28. Horizontal line through (−4, 0)
29. Horizontal line through (−4, −1)
30. Vertical line through (2, 3)
31. Vertical line through (−2, −1)
32. Horizontal line through (−5, −4)
33. Horizontal line through (4, 3)
34. Vertical line through (−3, −5)
35. Vertical line through (5, 2)
36. Horizontal line through (5, −1)

<a class=”internal” href=”/intermediatealgebraberg/back-matter/answer-key-3-6/”>Answer Key 3.6

3.7 Numeric Word Problems

For questions 1 to 8, write the formula defining each relationship. Do not solve.

1. Five more than twice an unknown number is 25.
2. Twelve more than 4 times an unknown number is 36.
3. Three times an unknown number decreased by 8 is 22.
4. Six times an unknown number less 8 is 22.
5. When an unknown number is decreased by 8, the difference is half the unknown number.
6. When an unknown number is decreased by 4, the difference is half the unknown number.
7. The sum of three consecutive integers is 21.
8. The sum of the first two of three odd consecutive integers, less the third, is 5.

For questions 9 to 16, write and solve the equation describing each relationship.

9. When five is added to three times a certain number, the result is 17. What is the number?
10. If five is subtracted from three times a certain number, the result is 10. What is the number?
11. Sixty more than nine times a number is the same as two less than ten times the number. What is the number?
12. Eleven less than seven times a number is five more than six times the number. Find the number.
13. The sum of three consecutive integers is 108. What are the integers?
14. The sum of three consecutive integers is −126. What are the integers?
15. Find three consecutive integers such that the sum of the first, twice the second, and three times the third is −76.
16. Find three consecutive odd integers such that the sum of the first, two times the second, and three times the third is 70.

<a class=”internal” href=”/intermediatealgebraberg/back-matter/answer-key-3-7/”>Answer Key 3.7