CHAPTER 3, 4, & 5 REVIEW

January 10, 2012

1. Solve + 5 = 11.x2

Write original equation.+ 5 = x2

11

+ 5 – 5 = x2 11 – 5 Subtract 5 from each side.

= x2

6 Simplify.

2 =x2 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.

8x – 3x – 10 = 20

8x – 3x – 10 = 20 Write original equation.

5x – 10 = 20 Combine like terms.

5x – 10 + 10 = 20 + 10 Add 10 to each side.

5x = 30 Simplify.

Divide each side by 5.

x = 6 Simplify.

= 305

5x5

Solve

Write original equation.

7d + 4 = 32 Combine like terms.

7d + 4 – 4 = 32 – 4 Subtract 4 from each side.

7d = 28 Simplify

Divide each side by 7.

d = 4 Simplify.

= 287

7d7

9d – 2d + 4 = 32

9d – 2d + 4 = 32

2. Solve the equation. Check your solution.

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

x280

= 8 amount of food100 weight of seal

Write a proportion involving two ratios that compare the amount of food with the weight of the seal.

Seals

STEP 2Solve the proportion.

8100

x280

= Write proportion.

8 280 = 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 perday.

b. lasagna

a. macaroni and cheese

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.

Survey

Solve for x.x = 15%

Use cross products.

Substitute 33 for is and 220 for of.

Write percent equation.

SOLUTION

3300 = 220x

The survey results show that 33 of the 220 students chose macaroni and cheese.

a.

is = %of = 100

33 = x220 =100

ANSWER

15% of the students chose macaroni and cheese as their favorite dish.

b. The survey results show that 40 of the 220 students chose lasagna.

Solve for x.x = 18%

Use cross products.

Substitute 40 for is and 220 for of.

Write percent equation.

4000 = 220x

is = %of = 100

40 = x220 =100

About 18% of the students chose lasagna as their favorite dish.

ANSWER

‾ b = ‾ 8/5y + 16

8/5y = b + 16

(8/5) y = (8/5) (5/8b + 10)

SOLUTION

5. Solve y = 5/8 b + 10 for b.

‾ 1 (‾ b) = ‾ 1 (‾ 8/5y + 16)

b = 8/5y - 16

Solve the equation for y.

SOLUTION

6. Graph the equation – 2x + y = – 3.

– 2x + y = – 3y = 2x – 3

STEP 1

Substitute 0 for y.

Write original equation.

To find the x-intercept, substitute 0 for y and solve for x.

SOLUTION

7. Find the x-intercept and the y-intercept of the graph of 2x + 7y = 28.

Solve for x.

2x + 7(0) = 28

x = = 14282

2x + 7y = 28

2(0) + 7y = 28

To find the y-intercept, substitute 0 for x and solve for y.

Write original equation.

Substitute 0 for x.

Solve for y.

ANSWER

The x-intercept is 14. The y-intercept is 4.

2x +7y = 28

y = 287 = 4

Let (x1, y1) = (–2, 3) = (x2, y2) = (4, 6).

m =y2 – y1

x2 – x1

(6) – 34 – (–2)

=

Simplify.

Substitute.

Write formula for slope.

8. Find the slope of the line with these two points (–2, 3) and (4, 6)

= 3 6

= 1 2

9. Find the slope of the line shown.

m =y2 – y1

x2 – x1

Let (x1, y1) = (3, 5) and (x2, y2) = (6, –1).

–1 – 56 – 3

=

– 63= = –2

Write formula for slope.

Substitute.

Simplify.

*** Or, if given the graph, count your rise over run!

Identify the slope and y-intercept of the line with the given equation.

y = 3x + 410.

3x + y = 211.

The equation is in the form y= m x + b.So, the slopeof the line is 3, and the y-intercept is 4.

Rewrite the equation in slope-intercept form by solving for y.

3x + y = 2 Write original equation.

y= – 3x + 2 Subtract 3x from each side.

The line has a slope of – 3 and a y-intercept of 2.

12. Graph y + 2x = 4

ANSWER

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 0

(–2, 6) and (4, –3)

ANSWER 32–

15.

Identify the slope and y-intercept of the line 2x + 4y = –16.

16. y = + 123

x

ANSWER

12

–Slope: ,y-intercept: –4ANSWER

17. Which equation represents the line shown?

The line crosses the y-axis at (0, 3). So, the y-intercept is 3.

y = mx + b Write slope-intercept form.

2y = – x + 35

2Substitute – for m and 3 for b.5

= = –The slope of the line is riserun

–2 5

25

.

A y = – x + 325 B y = – x + 35

2

C y = – x + 125 D y = 3x +

25

The correct answer is A. B DCA

18. Write an equation of the line that passes through the point (6, 3) and has a slope of 2.

SOLUTION

y = m x + b Write slope-intercept form.

Substitute 3 for y, 2 for m and 6 for x.

3 = 2(6) + b

Identify the slope. The slope is 2.STEP 1

Find the y-intercept. Substitute the slope and the coordinates of the given point in y = m x + b. Solve for b.

STEP 2

– 9 = b Solve for b.

y = m x + b Write slope-intercept form.

Substitute 2 for m and – 9 for b.y = 2x – 9

Write an equation of the line.STEP 3

19. Write an equation of the line that passes through (1, –2) and (–5, 4).

SOLUTION

Calculate the slope.

m = y2 – y1x2 – x1

= 4 –(– 2) –5 – 1

= 6–6

= – 1

Find the y-intercept. Use the slope and the point (1, –2).

y = m x + b Write slope-intercept form.

STEP 1

STEP 2

– 1 = b Solve for b.

y = m x + b Write slope-intercept form.

Substitute – 1 for m and – 1 for b.y = – x – 1

Write an equation of the line.STEP 3

–2 = –1(1) + b Substitute – 2 for y and – 1 for m.

20. Write an equation in point-slope form of the line that passes through the point (4, –3) and has a slope of 2.

y – y1 = m (x – x1) Write point-slope form.

y + 3 = 2 (x – 4) Substitute 2 for m, 4 for x1, and –3 for y1.

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.

Write an equation in point-slope form of the line that passes through the point (– 1, 4) and has a slope of – 2 .

21.

SOLUTION

22. Write an equation of the line that passes through (–3,–5) and is parallel to the line y = 3x – 1.

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 2Find the y-intercept. Use the slope and the given point.

y = mx + b

– 5 = 3(– 3) + b

4 = b

Write slope-intercept form.

Substitute 3 for m, -3 for x, and -5 for y.

Solve for b.

STEP 3

Write an equation. Use y = mx + b.

y = 3x + 4 Substitute 3 for m and 4 for b.

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.

23. Write an equation of the line that passes through

(–2, 11) and is parallel to the line y = – x + 5.

y = mx + b

11 = (–1 )(– 2) + b

9 = b

Write slope-intercept form.

Substitute 11 for y, – 1 for m, and – 2 for x.

Solve for b.

STEP 3

Write an equation. Use y = m x + b.

y = – x + 9 Substitute – 1 for m and 9 for b.

24. Solve the equation.

3x + 17 – 5x = 12 – (6x + 3)

A. x = ‾ ½

B. x = ‾ 1

C. x = ‾ 2

D. x = ‾ 4/7

25. Solve the proportion.

3 = 5

x – 4 x

26. Write an expression.

Three times the difference of a number x and 5.

27. Simplify.

30 – 18x

6

28. Find the MPG.

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

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

30. For which value of x is the relationship not a function?

{(1,2), (x,1), (4,6), (3,7)}

A. 2 B. 4 C. 5 D. 6*** Use MAP DIAGRAM!!!

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