1. Write the ratio 12 : 9 as an equivalent ratio of 4 : x. Write your answer as a complete ratio.
____.
2. Which of the following, Option 1 or Option 2, is a proportion?
Option 1: 5/6 = 15/18
Option 2: 5/6 = 20/18
Option ____ is a proportion.
3. Use the table to answer the question.
Cost of Ground Beef:
Pounds Cost ($)
10 -------- 37.50
8 ---------- 30.00
6 ---------- 22.50
4 ---------- 15.00
What is the cost for 1 pound of ground beef?
$ ____.
4. There are 48 inches in 4 feet, which is represented by the equation 4y = 48x. Determine the number of inches per foot.
____ inches.
5. A graph shows the proportional relationship. Derive the equation of the line y = mx through the origin.
There's a point at (5, 1) and a point at (10, 2).
____.
6. Graph the proportional relationship y = 2x by plotting points.
Responses:
A. A graph with the coordinates of (0, 0), (1, 2), (2, 4).
B. A graph with the coordinates of (0, 0), (1, 4).
C. A graph with the coordinates of (0, 0), (1, 3), (2, 6).
D. A graph with the coordinates of (0, 0), (2, 1).
7. The number of ushers at a basketball game is directly proportional to the number of spectators. If there are 510 spectators at the game, 17 ushers are needed. How many ushers are needed if there are 1,050 spectators?
Responses:
A. 31,500 ushers.
B. 35 ushers.
C. 32 ushers.
D. 315 ushers.
8. The proportional relationship between calories and ounces of soda is shown in the table below. How many calories are in 1 ounce?
Calories - Ounces
0 ---------------- 0
36 -------------- 3
72 -------------- 6
108 ------------ 9
144 ----------- 12
There are ____ calories in 1 ounce of soda.
9. The earnings for Employee 1 and Employee 2 are displayed in the following tables. Which employee earns more per hour?
Employee 1 - Earnings per Hour:
Employee - Hours
25 ---------------- 2
50 ---------------- 4
75 ---------------- 6
Employee 2 - Earnings per Hour:
Employee - Hours
15 ---------------- 1
45 ---------------- 3
75 ---------------- 5
Employee ____ earns more per hour.
10. Use similar triangles to determine the slope of the line.
The coordinates are: (0, 0), (1, 3), (2, 6), (3, 9).
The slope is ____.
11. Use the table to answer the question.
($) Cost of Candy Bar A:
Quantity - ($) Cost
1 -------------- 1.25
2 -------------- 2.50
3 -------------- 3.75
4 -------------- 5.00
5 -------------- 6.25
The cost of Candy Bar A is displayed in the table. The proportional relationship between the cost and quantity for Candy Bar B is represented by the equation y = x. Which candy bar is the cheapest cost per bar? Enter 1 for Candy Bar A. Enter 2 for Candy Bar B.
____.
12. Use the graph to derive the equation of the line in slope-intercept form.
The coordinates are (0, -2), (1, 3).
____.
13. Use the table to answer the question.
x y
−5 0
0 5
2 7
Which linear equation represents this non-proportional linear relationship?
Responses:
A. y = −5x + 5.
B. y = x + 5.
C. y = 1/5x + 5.
D. y = −x + 5.
14. The table shows the number of parts, y, a machine produces each hour, x. Write an equation for this situation, and indicate if this is proportional or non-proportional.
y (number of parts) x (number of hours)
0 ------------------------------------------- 0
125 --------------------------------------- 1
250 --------------------------------------- 2
375 --------------------------------------- 3
500 --------------------------------------- 4
Responses:
A. y = 125x + 1, nonproportional.
B. y = x + 125, nonproportional.
C. y = 125x, proportional.
D. y = 125x, nonproportional.
15. Write y − 6x = 5 in slope-intercept form
y = ____.
16. Graph the equation x − y = 6 using the form y = mx + b.
Responses:
A. A graph with the coordinates of (0, -6), (1, -5).
B. A graph with the coordinates of (0, -4), (1, -10).
C. A graph with the coordinates of (0, 3), (3, 2).
D. A graph with the coordinates of (0, 0), (6, 6).
Answer the multiple choice questions by A or B or C or D and answer the fill in the blank questions as the original answer.
A proportion is a mathematical relationship between two equal ratios. In a proportion, the cross products are equal, meaning that the product of the first term in one ratio and the second term in the other ratio is equal to the product of the second term in the first ratio and the first term in the second ratio. An example of a proportion is 2/3 = 4/6, where the cross products (2 x 6 and 3 x 4) are both equal to 12. This shows that the two ratios are proportional to each other. Proportions are used in various mathematical operations, including solving for unknown values in real-world situations.
1. 4 : 3.
2. Option 1 is a proportion.
3. $3.75.
4. 12 inches per foot.
5. y = (1/5)x.
6. A. A graph with the coordinates of (0, 0), (1, 2), (2, 4).
7. B. 35 ushers.
8. 12 calories in 1 ounce of soda.
9. Employee 1 earns more per hour.
10. The slope is 3.
11. 2. Candy Bar B is the cheapest cost per bar.
12. y = 5x - 2.
13. B. y = x + 5.
14. C. y = 125x, proportional.
15. y = 6x + 5.
16. A. A graph with the coordinates of (0, -6), (1, -5).