ANSWER KEYS - Teacher Use Only

Proportional Relationships | Grade 7

Student Concept Worksheet Answers
1
Yes, Proportional | k = 5 | Equation: y = 5x
Check: 10/2=5, 20/4=5, 30/6=5, 40/8=5. All ratios equal 5, so it's proportional with k=5.
2
a) k = 60 | b) y = 60x | c) 300 miles
k = 180/3 = 60 miles per hour. For 5 hours: y = 60(5) = 300 miles.
3
A) y = 4x, C) y = x/2, E) y = 0.5x
Only equations in the form y = kx (no added constants) are proportional. B has +1, D has no x variable. Note: y = x/2 = 0.5x, which is proportional with k = 0.5.
4
k = 12/4 = 3 | Equation: y = 3x
Use the point (4, 12): k = y/x = 12/4 = 3.
Practice Worksheet Answers

Part A: Identifying from Tables

# Answer Explanation
1Yes, k = 0.60, y = 0.60x0.60/1=0.60, 1.20/2=0.60, etc. All ratios = 0.60
2No, NOT proportional3/0 undefined; also 5/1=5, 7/2=3.5, 9/3=3. Ratios not equal. The $3 base fee makes it non-proportional.
3Yes, k = 25, y = 25x50/2=25, 125/5=25, 200/8=25, 250/10=25. All equal 25.

Part B: Finding k

4
k = 7
In y = 7x, the coefficient of x is k.
5
k = 1/4 or 0.25
In y = (1/4)x, k = 1/4 = 0.25.
6
k = 18/3 = 6
Use the point: k = y/x = 18/3 = 6.
7
k = 6/8 = 3/4 or 0.75
k = y/x = 6/8 = 0.75.

Part C: Writing Equations

#AnswerExplanation
8y = 32x32 miles per gallon means k = 32.
9y = 14.50x$14.50 per hour means k = 14.50.
10y = 12x12 eggs per carton means k = 12.
11y = 25x25 pages per minute means k = 25.

Part D: Identifying Proportional Equations

#EquationAnswerExplanation
12y = 6xYESForm y = kx with k = 6
13y = x + 5NOHas +5; doesn't pass through origin
14y = 2.5xYESForm y = kx with k = 2.5
15y = 4x - 4NOHas -4; doesn't pass through origin
16y = x/3YESSame as y = (1/3)x, k = 1/3

Part E: Word Problems

17
a) k = 3 | b) y = 3x | c) 30 feet
k = 12/4 = 3 feet per minute. For 10 min: y = 3(10) = 30 feet.
18
Yes, proportional. k = 3/2 = 1.5 cups flour per cup sugar
3 cups flour for 2 cups sugar means k = 3/2 = 1.5.
19
k = 7 | y = 7x | When x = 12, y = 84
k = 35/5 = 7. Equation: y = 7x. When x = 12: y = 7(12) = 84.
20
Yes, proportional | y = 9.50x | $76
k = 9.50 (price per ticket). Cost of 8 tickets: y = 9.50(8) = $76.

Challenge Questions:

#21: Jake is correct! Perimeter = 4 times side length. If s = side, P = 4s. This is y = kx with k = 4. When s = 0, P = 0 (passes through origin). Example: s = 1, P = 4; s = 2, P = 8; s = 3, P = 12. All have ratio 4.

#22: Runner A: k = 8 mph. Runner B: k = 42/6 = 7 mph. Since 8 > 7, Runner A is faster.

FAST Practice Quiz Answers
1
A) Table A only
Table A: 4/1=4, 8/2=4, 12/3=4. All equal, so proportional. Table B: 3/1=3, 5/2=2.5, 7/3=2.33. Not equal, so NOT proportional.
2
A) 4.5
In y = 4.5x, the coefficient of x is k. k = 4.5.
3
A) d = 70t
k = 210 miles / 3 hours = 70 mph. Equation: d = 70t. Option B has +210 (not proportional). Option C inverts the relationship. Option D uses wrong k.
4
Select: y = 8x, y = x/5, y = 0.25x
y = 8x - Yes, k = 8
y = x + 8 - No, has +8
y = x/5 - Yes, same as y = 0.2x, k = 0.2
y = 3x - 1 - No, has -1
y = 0.25x - Yes, k = 0.25
5
C) 2.5
k = y/x = 15/6 = 2.5. The constant of proportionality is always y divided by x.
6
A) It is always a straight line that passes through the origin (0, 0)
Proportional relationships have two key features: (1) straight line, and (2) passes through origin. B is too general (could be y = x + 5). C is wrong point. D is wrong shape.
FAST Quiz Scoring Guide
Score Interpretation Recommended Action
6/6 Mastery Ready for solving proportional relationship word problems and connecting to slope.
4-5/6 Approaching Mastery Review specific misconception (calculating k, identifying from equations, or understanding graphs).
2-3/6 Developing Reteach using tables first. Practice finding y/x for each row. Emphasize the "same ratio" requirement.
0-1/6 Needs Intervention Small group instruction. Review ratios and unit rates. Use real-world examples (speed, price per unit) before abstract equations.
FAST Success Kit | Grade 7 | FL B.E.S.T. Standards: MA.7.AR.4.1, MA.7.AR.4.2, MA.7.AR.4.3 | Answer Key - Teacher Use Only