**Directions**: Please show all of your work for each problem. If applicable, you may find Microsoft Word’s equation editor helpful in creating mathematical expressions in Word. There is a tutorial on using this equation editor in Module 1 Lecture Notes. You also have the option of hand writing your work and scanning it.

1. Find the *y*-intercept of the line represented by the following equation. –2*x* + 2*y* = 16

2. Write the equation of the line with slope –4 and *y*-intercept (0, –9).

3. Write the equation of the line with slope and *y*-intercept (0, 3).

4. One day, the temperature at 9:00 A.M. was 49°F, and by 3:00 P.M. the temperature was 61°F. What was the hourly rate of temperature change?

5. Determine which two equations represent parallel lines.

(a) *y* = –7*x* + 3 (b) *y* = 7*x* + 3 (c) *y* = *x* + 3 (d) *y* = –7*x* + 6

6. Determine which two equations represent perpendicular lines.

(a) *y* = *x* – 5 (b) *y* = 5*x* – (c) *y* = *x* + (d) *y* = *x* –

7. Are the following lines parallel, perpendicular, or neither?

*L*_{1} through (–4, –7) and (1, 3)

*L*_{2} through (2, 6) and (4, 10)

8. Are the following lines parallel, perpendicular, or neither?

*L*_{1} with equation *x – *5*y* = 25

*L*_{2} with equation 5*x + y* = 5

9. Find the slope of any line perpendicular to the line through points (8, 4) and (9, 7).

10. A line passing through (6, –10) and (–1, *y*) is perpendicular to a line with slope . Find the value of *y*.

11. Use the concept of slope to determine whether the given figure is a right triangle (i.e., does the triangle contain a right angle?).

12. Write the equation of the line that passes through point (0, 9) with a slope of 6.

13. Write the equation of the line passing through (1, –8) and (1, 3). Write your results in slope-intercept form, if possible.

14. Write the equation of the line with *x*-intercept (–9, 0) and undefined slope. Write your results in slope-intercept form, if possible.

15. A copier was purchased by a company for $7,500. After 5 years it is estimated that the value of the copier will be $4,500. If the value in dollars *V* and the time the copier has been in use *t* are related by a linear equation, find the equation that relates *V* and *t*.

16. You have at least $60 in change in your piggy bank, consisting of quarters and pennies. Write an inequality that shows the different number of coins in your piggy bank.

17. If *f*(*x*) = –*x*^{3} – *x*^{2} + 2*x* + 6, find *f*(–2), *f*(0), and *f*(3)

18. Rewrite the equation *y* = 2*x* + 2 as a function of *x*.

19. The inventor of a new product believes that the cost of producing the product is given by the function: *C*(*x*) = 2.75*x* + 2,000. How much does it cost to produce 6,000 units of his invention?

20. Given *f*(*x*) = –5*x* + 3, find *f*(*a* + 1).

21. Write the equation of a line that passes through (0, 4) and has a slope of -1/5.

22. Write the equation of a horizontal line with a y-intercept of 7.

23. What is the slope and the y-intercept of y=3x+1?

24. What is the slope and y-intercept of y=-3?

25. What is the slope and y-intercept of 6x+y=10?

26. Determine whether the lines are parallel, perpendicular, or neither.

Y=-3x+1

Y=-3x-8

27. Determine whether the lines are parallel, perpendicular, or neither.

2x-y=-10

2x+4y=2

28. Determine whether the lines are parallel, perpendicular, or neither.

Line 1 passes through (0, 3) and (2, 5)

Line 2 passes through (5, -4) and (-3, 3)

29. Write the equation of a line that passes through (4, 0) and (-4, -5). Write your answer in slope-intercept form.

30. Write the equation of a line that passes through (-1, 2) and (3, 5). Write your answer in slope-intercept form.

31. Write the equation of a line that passes through (1, -45) with a slope of -3. Write your answer in slope-intercept form.

32. Write the equation of a line that passes through (-2, 5) with a slope of -4. Write your answer in slope-intercept form.

33. Write the equation of a line that passes through (-2, 5) and (-6, 13). Write your answer in slope-intercept form.

34. f(x)=1/2x Find f(0)

35. f(x) = 4x^2+3x Find f(-2)

36. f(x)=3x+3 Find f(-1)

37. f(x)=5x^2-7 Find f(0)