7th Grade Proportional Relationships and y = kx Quiz: 10 Questions with Explanations

A \(x\): 2, 4, 6 and \(y\): 6, 12, 18B \(x\): 1, 2, 3 and \(y\): 4, 6, 8C \(x\): 1, 2, 3 and \(y\): 3, 5, 7D \(x\): 2, 4, 6 and \(y\): 5, 9, 13

Only the first has equal ratios (all 3). The others have changing ratios because they add a fixed amount instead of multiplying.

A \(4.5\)B \(14\)C \(22\)D \(72\)

\(k = y \div x = 18 \div 4 = 4.5\). Subtracting or multiplying does not give the ratio.

A \(y = x + 2.5\)B \(y = 2.5x\)C \(y = x/2.5\)D \(y = 2.5/x\)

A constant cost per mile means y is x times 2.5. Dividing by 2.5 would give miles per dollar.

A It is a straight line through the originB It is any straight lineC It is a curve through the originD It is a line that crosses the y-axis at 1

Both conditions are needed. A straight line that misses the origin, such as \(y = x + 1\), is not proportional.

A \((1, 15)\)B \((1, 4)\)C \((1, 25)\)D \((1, 5)\)

\(k = 20 \div 5 = 4\), so \((1, 4)\) is on the graph. Subtracting 5 from both coordinates is a common error.

A The y-interceptB The number of x-valuesC The constant of proportionalityD The sum of x and y

In \(y = kx\), k is the multiplier, the unit rate. The graph passes through the origin, so there is no y-intercept other than 0.

A \(24.4\)B \(41.67\)C \(25.6\)D \(15\)

Multiply: \(0.6 \times 25 = 15\). Dividing 25 by 0.6 solves for x from y.

A The distance is proportional to time with k = 55B The distance is proportional to time with k = 60C The distance is proportional to time with k = 65D The distance is not proportional to time

\(55 \div 1 = 55\) but \(120 \div 2 = 60\). The ratios differ, so it is not proportional.

A \(1\frac{1}{2}\) cupsB \(3\) cupsC \(2\frac{1}{4}\) cupsD \(6\frac{3}{4}\) cups

\(k = \frac{3}{4} \div 2 = \frac{3}{8}\), and \(\frac{3}{8} \times 6 = \frac{9}{4} = 2\frac{1}{4}\). Adding 4 servings to the rice is an additive mistake.

A 1 hour earns $0B 0 hours earns $0C $0 earns 1 hourD the unit rate is 0

The origin pairs zero hours with zero dollars. The unit rate is shown by the point \((1, k)\).