Equations of Proportional Relationships: Grade 7 Math Test Answer Key – PDF Download

Question 1: Constant from a table (2 points)

\(\frac{18}{4}=4.5\), \(\frac{36}{8}=4.5\), \(\frac{54}{12}=4.5\).

1. \(k=4.5\)
2. \(y=4.5x\)

Scoring: 1 point for the correct constant (a); 1 point for the correct equation (b). Accept \(y=\frac{9}{2}x\).

Question 2: Equation from a graph (2 points)

Use the point \((4,3)\): \(k=\frac{3}{4}=0.75\). Check: \(\frac{6}{8}=0.75\) and \(\frac{9}{12}=0.75\).

1. \(k=0.75\)
2. \(y=0.75x\)

Scoring: 1 point for \(k\) (accept \(\frac{3}{4}\)); 1 point for the equation.

Question 3: Notebooks (2 points)

1. \(t=1.85n\)
2. \(t=1.85\times 12=22.2\), so the cost is $22.20.

Scoring: 1 point for the equation; 1 point for $22.20 (with the unit or dollar sign).

Question 4: Two tables (3 points)

Table A: \(\frac{7}{2}=3.5\), \(\frac{14}{4}=3.5\), \(\frac{21}{6}=3.5\). Table B: \(\frac{4}{1}=4\), \(\frac{7}{2}=3.5\), \(\frac{10}{3}\approx 3.33\).

1. Table A is proportional (all ratios equal 3.5). Table B is not proportional (the ratios 4, 3.5 and 3.33 differ).
2. \(y=3.5x\)

Scoring: 1 point for each correct decision with a justification using ratios (2 points in all); 1 point for \(y=3.5x\).

Question 5: Hourly pay (2 points)

1. \(p=13.5\times 18=243\), so $243.00.
2. \(202.5=13.5h\), so \(h=202.5: 13.5=15\) hours. Check: \(13.5\times 15=202.5\).

Scoring: 1 point for $243; 1 point for 15 hours.

Question 6: Two printers (3 points)

1. \(\frac{40}{2}=20\), \(\frac{100}{5}=20\), \(\frac{160}{8}=20\), so \(p=20m\).
2. Printer A prints 18 pages per minute and Printer B prints 20, so Printer B is faster.
3. In 15 minutes: A prints \(18\times 15=270\) pages and B prints \(20\times 15=300\) pages. B prints 30 more pages.

Scoring: 1 point for the equation; 1 point for comparing 18 with 20 and naming Printer B; 1 point for 30 pages.

Question 7: Dog walking (3 points)

Use the point \((3,24)\): \(k=\frac{24}{3}=8\).

1. \(y=8x\)
2. The point \((1,8)\) means Ethan earns $8 for 1 hour of dog walking, which is the unit rate.
3. Ethan: \(8\times 6=48\). Mei: \(7.5\times 6=45\). Ethan earns $3 more.

Scoring: 1 point for the equation; 1 point for stating $8 per hour; 1 point for Ethan earning $3 more.

Question 8: Filling a tank (3 points)

1. \(k=\frac{30}{8}=3.75\), so \(g=3.75m\).
2. \(3.75\times 25=93.75\) gallons.
3. \(150=3.75m\), so \(m=150: 3.75=40\) minutes.

Scoring: 1 point for the equation; 1 point for 93.75 gallons; 1 point for 40 minutes.

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