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HomeWork

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. –2x + 2y = 16

2y=16

Y=8

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

Y = -4x - 9

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

Y = -x/2 + 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?

(61 – 49) / 6 = 2 deg/h

5. Determine which two equations represent parallel lines.

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

(a) and (d) are parallel, same slope

6. Determine which two equations represent perpendicular lines.

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

(b) and (c) are perpendicular

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 equation x – 5y = 25

L2 with equation 5x + y = 5

They are perpendicular, slope = 1/5 and -5

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

(7 – 4) / ( 9 – 8) = 3

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

(y + 10) / (-1 – 6) = -2/7

Y + 10 = 2

Y = -8

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?).

Yes it is a right triangle

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

Y = 6x + 9

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

Slope undefined

X = 1

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

X = -9

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.

3000 / 5 = 600

V = 7500 – 600t

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.

25q + p ≥ 6000

17. If f(x) = –x3 – x2 + 2x + 6, find f(–2), f(0), and f(3)

f(-2) = 6 -(-2)^3 - (-2)^2 + 2(-2) + 6 = +8 -4 -4 + 6 = 6 f(0) = 6 –(0)3 –(0)2 + 2(0)+ 6 = 6 f(3) = 24 –(3)3 –(3)2 + 2(3) + 6 = -27-9+6+6 = 24

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

Y = 2x + 2

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?

C(6000) = (2.75)(6000) + 2000 = 18500

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

F(a+1) = -5(a+1) + 3 = -5a – 2

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

Y = -x/5 + 4

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

Y = 7

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

Slope = 3

y-intercept = 1

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

Slope = 0

y-intercept = -3

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

Slope = -6

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.

Slope = -5 / -8 = 5/8

Y = 5/8(x-4) = 5x/8 – 5/2

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

Slope = 3 / 4

Y – 2 = 3/4 (x+1)

Y = 3x/4 + 11/4

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

Y + 45 = -3(x – 1)

Y = -3x – 42

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

Y – 5 = -4(x+2)

Y = -4x - 3

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

Slope = (13-5)/(-6+2) = -2

y-5 = -2(x+2)

y = -2x + 1

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

F(0)=0

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

F(-2) = 4(4)+3(-2) = 10

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

F(-1) = -3+3=0

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

F(0) = -7