CHAPTER 3, 4, & 5 REVIEW

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

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

3. 5x 30 = 5 5 Solve 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.

4. 9d – 2d + 4 = 32 7d 28 = 7 7 2. Solve the equation. Check your solution. 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 Divide each side by 7. d = 4 Simplify.

5. x 280 8 amount of food = weight of seal 100 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.

6. = 8 280 = 100 x x ANSWER 8 280 100 A280pound seal should be fed22.4pounds of food per day. STEP 2 Solve the proportion. Write proportion. Cross products property 2240 = 100x Simplify. 22.4 = x Divide each side by 100.

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

9. ANSWER About 18% of the students chose lasagna as their favorite dish. 220x 4000 = b. The survey results show that40of the220 students chose lasagna. is = % Write percent equation. of = 100 40 = x Substitute 40 for isand 220 for of. 220 =100 Use cross products. x = 18% Solve for x.

10. 5. Solve y = 5/8 b + 10 forb. SOLUTION (8/5) y = (8/5) (5/8b + 10) 8/5y = b + 16 ‾ 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. 2x + 7y= 28 28 x = = 14 2 7. Find the x-intercept and the y-intercept of the graph of 2x+7y=28. SOLUTION To find the x-intercept, substitute 0 foryand solve forx. Write original equation. 2x + 7(0) = 28 Substitute0fory. Solve for x.

13. 2x+7y = 28 28 4 y = = 7 ANSWER The x-intercept is 14. They-interceptis 4. To find they-intercept,substitute0forx and solve fory. Write original equation. 2(0) + 7y = 28 Substitute 0 for x. Solve fory.

14. 1 2 (6) – 3 = 4– (–2) y2 –y1 m = x2 – x1 3 = = 6 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). Write formula for slope. Substitute. Simplify.

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

16. 3x + y =2 y = – 3x + 2 10. y = 3x + 4 11. 3x +y = 2 The line has a slope of – 3 and a y-intercept of 2. The equation is in the formy =m x +b. So, the slope of the line is 3, and they-intercept is4. Rewrite the equation in slope-intercept form by solving for y. Identify the slope and y-intercept of the line with the given equation. Write original equation. Subtract 3xfrom each side.

17. ANSWER 12.Graphy + 2x = 4

18. ANSWER 0 x-int: 1, y-int: – 3 ANSWER 3 – ANSWER 2 13. Find thex-intercept and they-intercept of thegraphof 3x – y = 3 14. Find the slope of the line that passes through the points (12, – 1)and (–3, – 1) (–2, 6) and(4, –3)

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

20. y =–x+ 3 y =–x+ 3 The correct answer is A. y =–x+ 1 y =3x + A B C D 2 5 2 2 2 –2 5 5 5 2 The slope of the line is . – = = 5 rise 5 run A C B D 2 2 y= –x+3 Substitute– for mand3forb. 5 5 17. Which equation represents the line shown? The line crosses they-axisat(0, 3).So, they-intercept is3. y =mx +b Write slope-intercept form.

21. 18. Write an equation of the line that passes through the point (6, 3) and has a slope of2. SOLUTION STEP1 Identify the slope. The slope is2. Find the y-intercept. Substitute the slope and the coordinates of the given point in y = m x +b. Solve for b. STEP2 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. STEP3 Write an equation of the line. y =m x+ b Write slope-intercept form. y = 2x – 9 Substitute 2 for mand –9 for b.

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

24. (1) + b –2= –1 Substitute– 2foryand– 1form. –1=b Solve for b. STEP3 Write an equation of the line. y =m x+ b Write slope-intercept form. y = – x – 1 Substitute –1 for mand –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) Substitute2form,4 for x1, and–3 fory1.

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

27. 22. Write an equation of the line that passes through (–3,–5)and is parallel to the liney= 3x– 1. SOLUTION STEP1 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. STEP2 Find the y-intercept. Use the slope and the given point.

28. y=mx+b Write slope-intercept form. – 5=3(–3) +b Substitute3form,-3for x,and-5fory. Solve forb. 4 = b STEP3 Write an equation. Usey = mx + b. Substitute3formand4forb. y = 3x + 4

29. 23. Write an equation of the line that passes through (–2, 11) and is parallel to the liney=–x+ 5. SOLUTION STEP1 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. STEP2 Find the y-intercept. Use the slope and the given point.

30. y=mx+b Write slope-intercept form. 11= (–1 )(–2) +b Substitute11fory,– 1form,and–2forx. Solve forb. 9 = b STEP3 Write an equation. Usey = m x + b. y = –x + 9 Substitute– 1formand9forb.

31. 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. 3 = 5 x – 4 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? {(1,2), (x,1), (4,6), (3,7)} A. 2 B. 4 C. 5 D. 6 *** Use MAP DIAGRAM!!! input output