1. CHAPTER 3, 4, & 5 REVIEW
January 10, 2012

2. 1. Solve + 5 = 11. x 2 + 5 = x 2 11 + 5 – 5 = x 2 11 – 5 = x 2 6 2 = x
Write original equation.
+ 5 – 5 = x 2
11 – 5
Subtract 5 from each side. = x 2 6
Simplify. = x 2
2 6
Multiply each side by 2.
x = 12
Simplify.
ANSWER
The solution is 12. Check by substituting 12 for x in the original equation.

3. Solve
8x – 3x – 10 = 20
8x – 3x – 10 = 20
Write original equation.
5x – 10 = 20
Combine like terms.
5x – =
Add 10 to each side.
5x = 30
Simplify. = 30 5 5x
Divide each side by 5.
x = 6
Simplify.

4. 2. Solve the equation. Check your solution.
9d – 2d + 4 = 32
9d – 2d + 4 = 32
Write original equation.
7d + 4 = 32
Combine like terms.
7d + 4 – 4 = 32 – 4
Subtract 4 from each side.
7d = 28
Simplify = 28 7 7d
Divide each side by 7.
d = 4
Simplify.

5. How much food should the seal be fed per day ?
Seals
3. Each day, the seals at an aquarium are each fed 8 pounds of food for every 100 pounds of their body weight. A seal at the aquarium weighs 280 pounds.
How much food should the seal be fed per day ?
SOLUTION
STEP 1
Write a proportion involving two ratios that compare the amount of food with the weight of the seal. x
280 = 8
amount of food
100
weight of seal

6. A 280 pound seal should be fed 22.4 pounds of food per day.
STEP 2
Solve the proportion. 8
100 x
280 =
Write proportion.
= 100 x
Cross products property
2240 = 100x
Simplify.
22.4 = x
Divide each side by 100.
ANSWER
A 280 pound seal should be fed 22.4 pounds of food per
day.

7. 83 Type of Pasta Students Spaghetti Lasagna 40 Macaroni and cheese 33
Survey
Type of Pasta
Students
Spaghetti 83
Lasagna 40
Macaroni and cheese 33
Fettucine alfredo 22
Baked ziti 16
Pasta primavera 15
Other 11
4. A survey asked 220 students to name their favorite pasta dish. Find the percent of students who chose the given pasta dish.
a. macaroni and cheese
b. lasagna

8. 15% of the students chose macaroni and cheese as their favorite dish.
SOLUTION
The survey results show that 33 of the 220 students chose macaroni and cheese. a.
is = %
Write percent equation.
of = 100
33 = x
Substitute 33 for is and 220 for of.
220 =100
3300 =
220x
Use cross products.
x = 15%
Solve for x.
ANSWER
15% of the students chose macaroni and cheese as their favorite dish.

9. b. The survey results show that 40 of the 220 students chose lasagna.
is = %
Write percent equation.
of = 100
40 = x
Substitute 40 for is and 220 for of.
220 =100
4000 =
220x
Use cross products.
x = 18%
Solve for x.
About 18% of the students chose lasagna
as their favorite dish.
ANSWER

10. 5. Solve y = 5/8 b + 10 for b. SOLUTION (8/5) y = (8/5) (5/8b + 10)
‾ b = ‾ 8/5y + 16
‾ 1 (‾ b) = ‾ 1 (‾ 8/5y + 16)
b = 8/5y - 16

11. 6. Graph the equation – 2x + y = – 3.
SOLUTION
STEP 1
Solve the equation for y.
– 2x + y = – 3
y = 2x – 3

12. To find the x-intercept, substitute 0 for y and solve for x.
7. Find the x-intercept and the y-intercept of the graph of 2x + 7y = 28.
SOLUTION
To find the x-intercept, substitute 0 for y and solve for x.
2x + 7y = 28
Write original equation.
2x + 7(0) = 28
Substitute 0 for y.
x =
= 14 28 2
Solve for x.

13. To find the y-intercept, substitute 0 for x and solve for y.
2x +7y = 28
Write original equation.
2(0) + 7y = 28
Substitute 0 for x.
y = 28 7 = 4
Solve for y.
ANSWER
The x-intercept is 14. The y-intercept is 4.

14. 8. Find the slope of the line with these two points (–2, 3) and (4, 6)
Let (x1, y1) = (–2, 3) = (x2, y2) = (4, 6).
m =
y2 – y1
x2 – x1
Write formula for slope.
(6) – 3
4 – (–2) =
Substitute. = 3 6 1 2
Simplify.

15. *** Or, if given the graph, count your rise over run!
9. Find the slope of the line shown.
Let (x1, y1) = (3, 5) and (x2, y2) = (6, –1).
m =
y2 – y1
x2 – x1
Write formula for slope.
–1 – 5
6 – 3 =
Substitute.
– 6 3 = –2
Simplify.
*** Or, if given the graph, count your rise over run!

16. The equation is in the form y = m x + b. So, the slope
Identify the slope and y-intercept of the line with the given equation.
y = 3x + 4
10.
The equation is in the form y
= m x + b.
So, the slope
of the line is 3, and the y-intercept is 4.
3x + y = 2
11.
Rewrite the equation in slope-intercept form by solving for y.
3x + y
= 2
Write original equation.
The line has a slope of – 3 and a y-intercept of 2. y
= – 3x + 2
Subtract 3x from each side.

17. Graph y + 2x = 4
ANSWER

18. 13. Find the x-intercept and the y-intercept of the graph of 3x – y = 3
x-int: 1, y-int: – 3
ANSWER
14. Find the slope of the line that passes through the points
(12, – 1) and (– 3, – 1)
ANSWER
(–2, 6) and (4, –3)
ANSWER 3 2 –

19. 15.
Identify the slope and y-intercept of the line 2x + 4y = –16. 1 2 –
Slope: ,y-intercept: –4
ANSWER
y = 2 3 x
ANSWER

20. 17. Which equation represents the line shown?
y = – x + 3 2 5 B C
y = – x + 1 D
y = 3x + = –
The slope of the line is
rise
run –2 5 2 .
The line crosses the y-axis at (0, 3). So, the y-intercept is 3.
y = mx + b
Write slope-intercept form. 2
y = – x + 3 5 2
Substitute – for m and 3 for b. 5
The correct answer is A. B D C A

21. Identify the slope. The slope is 2.
18. Write an equation of the line that passes through the point (6, 3) and has a slope of 2.
SOLUTION
STEP 1
Identify the slope. The slope is 2.
STEP 2
Find the y-intercept. Substitute the slope and the coordinates of the given point in y = m x + b. Solve for b.
y = m x + b
Write slope-intercept form.
3 = 2(6) + b
Substitute 3 for y, 2 for m and 6 for x.
– 9 = b
Solve for b.

22. Write an equation of the line.
STEP 3
Write an equation of the line.
y = m x + b
Write slope-intercept form.
y = 2x – 9
Substitute 2 for m and – 9 for b.

23. Find the y-intercept. Use the slope and the point (1, –2).
19. Write an equation of the line that passes through (1, –2) and (–5, 4).
SOLUTION
STEP 1
Calculate the slope.
m =
y2 – y1
x2 – x1 =
4 –(– 2)
–5 – 1 6 –6
– 1
STEP 2
Find the y-intercept. Use the slope and the point (1, –2).
y = m x + b
Write slope-intercept form.

24. Write an equation of the line.
–2 = –1
(1)
+ b
Substitute – 2 for y and – 1 for m.
– 1 = b
Solve for b.
STEP 3
Write an equation of the line.
y = m x + b
Write slope-intercept form.
y = – x – 1
Substitute – 1 for m and – 1 for b.

25. 20. Write an equation in point-slope form of the line that passes through the point (4, –3) and has a slope of 2.
Write point-slope form.
y – y1 = m (x – x1)
y + 3 = 2 (x – 4)
Substitute 2 for m, 4 for x1, and –3 for y1.

26. Write an equation in point-slope form of the line that passes through the point (– 1, 4) and has a slope of – 2 .
21.
y – y1 = m (x – x1)
Write point-slope form.
y – 4 = –2 (x +1)
Substitute – 2 for m, 4 for y, and –1 for x.

27. 22. Write an equation of the line that passes through
22. Write an equation of the line that passes through (–3,–5) and is parallel to the line y = 3x – 1.
SOLUTION
STEP 1
Identify the slope. The graph of the given equation has a slope of 3. So, the parallel line through (– 3, – 5) has a slope of 3.
STEP 2
Find the y-intercept. Use the slope and the given point.

28. Write an equation. Use y = mx + b.
Write slope-intercept form.
– 5 = 3(– 3) + b
Substitute 3 for m, -3 for x, and -5 for y.
4 = b
Solve for b.
STEP 3
Write an equation. Use y = mx + b.
y = 3x + 4
Substitute 3 for m and 4 for b.

29. 23. Write an equation of the line that passes through
(–2, 11) and is parallel to the line y = – x + 5.
SOLUTION
STEP 1
Identify the slope. The graph of the given equation has a slope of – 1.So, the parallel line through (– 2, 11) has a slope of – 1.
STEP 2
Find the y-intercept. Use the slope and the given point.

30. Write an equation. Use y = m x + b.
Write slope-intercept form.
11 = (–1 )(– 2) + b
Substitute 11 for y, – 1 for m, and – 2 for x.
9 = b
Solve for b.
STEP 3
Write an equation. Use y = m x + b.
y = – x + 9
Substitute – 1 for m and 9 for b.

31. 3x + 17 – 5x = 12 – (6x + 3) A. x = ‾ ½ B. x = ‾ 1 C. x = ‾ 2
24. Solve the equation.
3x + 17 – 5x = 12 – (6x + 3)
A. x = ‾ ½
B. x = ‾ 1
C. x = ‾ 2
D. x = ‾ 4/7

32. 25. Solve the proportion.
= 5
x – x

33. 26. Write an expression.
Three times the difference of a number x and 5.

34. 27. Simplify.
30 – 18x 6

35. 28. Find the MPG.
The red vette traveled 368 miles on 16 gallons of gas. What is the mpg of the vette?

36. 29. What’s my checking account balance?
Monday…wrote a check to Starbuck…$ 35
Tuesday…got a refund from Macy’s…$125
Wednesday…wrote a check to Sam’s…$ 45
Thursday…wrote a check for car…$ 895
Friday…wrote a check for dinner…$ 48

37. 30. For which value of x is the relationship not a function?
A. 2 B. 4 C. 5 D. 6
*** Use MAP DIAGRAM!!!
input output