41) If x increases whenever y decreases, then x and y are
A) not related.
B) positively related.
C) directly related.
D) negatively related.
E) related but whether positively or negatively related depends on whether the x variable or the y variable is plotted on the vertical axis.
42) Whenever one variable increases, another variable decreases. The two variables are
A) definitely related through a third variable.
B) negatively related.
C) positively related.
D) unrelated to each other.
E) related but whether positively or negatively related depends on which variable is plotted on the vertical axis.
43) If x increases and as a result y decreases, then x and y are
A) not related because the relationship is a causal one.
B) positively related.
C) negatively related.
D) directly related.
E) trend-line related.
44) “As the price of gasoline increases, fewer people buy cars that are gas guzzlers.” A graph showing this relationship would
A) have a negative slope.
B) have a positive relationship.
C) have a direct relationship.
D) be a horizontal line.
E) be a vertical line.
45) As the number of days without rain increases, the amount of wheat grown per acre declines. A graph showing this relationship shows
A) a horizontal line.
B) a vertical line.
C) a positive relationship.
D) a line with a positive slope.
E) None of the above answers is correct.
46) As the price of home heating oil rises, families buy less home heating oil. Hence a scatter diagram with the price of home heating oil on the vertical axis and the quantity purchased on the horizontal axis reveals a __ relationship.
A) positive
B) linear
C) time-series
D) negative
E) cross-sectional
47) If the change in y = -4 and the change in x = 2, there is
A) an independent relationship between y and x.
B) a positive relationship between y and x.
C) a negative relationship between y and x.
D) no relationship between y and x.
E) a relationship between x and y but more information is needed to determine if it is a negative or positive relationship.
48) An independent relationship between two variables is shown in a graph by
A) an upward-sloping line.
B) a horizontal or a vertical line.
C) a downward-sloping line.
D) a steeply sloped line.
E) any straight line curve.
49) If two variables are unrelated, their graph is
A) either a horizontal or a vertical line.
B) a downward-sloping line.
C) an upward-sloping line.
D) a curved line.
E) None of the above answers is correct because it is not possible to graph unrelated variables.
50) Consider a diagram in which the variable measured on the y-axis remains constant while the variable measured on the x-axis increases. The graph of these two variables is a
A) vertical line.
B) horizontal line.
C) line that has positive slope.
D) line that has a negative slope.
E) non-existent because the two variables are not related.
The Correct Answer and Explanation is :
Here are the correct answers with explanations:
41) D) negatively related.
Explanation: If ( x ) increases as ( y ) decreases, this indicates a negative relationship. In such cases, when one variable increases, the other decreases.
42) B) negatively related.
Explanation: If one variable increases while the other decreases, this indicates a negative relationship, as the change in one variable is opposite to the change in the other.
43) C) negatively related.
Explanation: A decrease in ( y ) when ( x ) increases suggests a negative relationship between the two variables, as they move in opposite directions.
44) A) have a negative slope.
Explanation: As the price of gasoline increases, fewer people will purchase gas-guzzling cars. The relationship between price and demand is inversely proportional, resulting in a negative slope on a graph.
45) E) None of the above answers is correct.
Explanation: The relationship between the number of dry days and wheat yield likely involves a decline in yield as the number of dry days increases, but the answer choices don’t fully capture the relationship, which could be a downward trend or other form of non-linear relationship.
46) D) negative.
Explanation: As the price of home heating oil increases, families buy less, showing a negative relationship. A graph of this relationship would show a downward-sloping curve.
47) C) a negative relationship between y and x.
Explanation: A negative change in ( y ) and a positive change in ( x ) indicates a negative relationship, meaning that as ( x ) increases, ( y ) decreases.
48) B) a horizontal or a vertical line.
Explanation: An independent relationship means that the change in one variable does not affect the other. A horizontal line shows no change in ( y ) as ( x ) changes, and a vertical line shows no change in ( x ) as ( y ) changes.
49) E) None of the above answers is correct because it is not possible to graph unrelated variables.
Explanation: Unrelated variables do not form any recognizable relationship that can be graphed, meaning there is no distinct graph for unrelated variables.
50) B) horizontal line.
Explanation: If the variable on the y-axis remains constant while the variable on the x-axis increases, the graph will be a horizontal line, since the value of ( y ) does not change as ( x ) changes.
Each answer is tied to the understanding of the relationship between variables—whether they increase or decrease in relation to one another, or remain unaffected, and how these relationships are represented on graphs.