7th Grade Proportional Relationships and y = kx Test Solutions and Scoring (PDF)

\(7.5\div 3=2.5,\; 12.5\div 5=2.5,\; 20\div 8=2.5\).

Yes; \(y=2.5x\)

Scoring: 1 point for comparing all the ratios; 1 point for the conclusion and the equation.

\(k=14\div 8=1.75\); \(y=1.75x\).

\(1.75\times 20=35\)

k = 1.75; y = 1.75x; y = 35

Scoring: 1 point for k and the equation; 1 point for y = 35.

1. The graph is a straight line through the origin (0, 0).
2. \(k=6\div 3=2\), so \(y=2x\).

Scoring: 1 point for each part.

\(6.5\times 2=13\); \(6.5\times 5=32.5\); \(6.5\times 12=78\).

13, 32.5, 78

Scoring: 1 point for using multiplication by 6.5; 1 point for all three correct values. Deduct nothing if the dollar sign is missing.

\(k=3\div 4=0.75\): $0.75 per pound.

\(0.75\times 10=7.5\).

$0.75; $7.50

Scoring: 1 point for the unit price; 1 point for the cost of 10 pounds.

\(y=8x\) and \(y=6x+5\).

With 0 cars the first costs $0 and the second costs $5, so only the first is proportional.

\(y=8x\) is proportional

Scoring: 1 point for both equations; 1 point for the correct choice with a reason.

\(k=\frac{1}{6}\div\frac{1}{4}=\frac{1}{6}\times 4=\frac{2}{3}\).

\(\frac{2}{3}\times\frac{1}{2}=\frac{1}{3}\) and \(\frac{2}{3}\times 1=\frac{2}{3}\).

Scoring: 1 point for k; 1 point for both missing values.

1. \(k=60\div 8=7.5\), so \(y=7.5x\).
2. \(7.5\times 5=37.5\), so $37.50.
3. \(150\div 7.5=20\) hours.

\(y=7.5x\); $37.50; 20 hours

Scoring: 1 point for each part.

1. A: \(12\div 2=6\). B: \(12\div 4=3\).
2. \(y=6x\) and \(y=3x\).
3. \(30-15=15\), so line A is greater by 15.

Scoring: 1 point for each part.