MAT 105 help again?

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

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

3. Write the equation of the line with slope andy-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 = –7x + 3 (b) y = 7x + 3 (c) y = x + 3 (d) y = –7x + 6

6. Determine which two equations represent perpendicular lines.

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

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

L₁ through (–4, –7) and (1, 3)

L₂ through (2, 6) and (4, 10)

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

L₁ with equationx –5y = 25

L₂ with equation 5x + 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 ofy.

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 withx-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 dollarsV and the time the copier has been in use t are related by a linear equation, find the equation that relatesV andt.

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. Iff(x) = –x³ –x² + 2x + 6, findf(–2),f(0), andf(3)

18. Rewrite the equationy = 2x + 2 as a function ofx.

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

20. Givenf(x) = –5x + 3, findf(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)