Question

What is the difference between a graph representing data that are directly proportional and a graph of data that are inversely proportional?

A. Directly proportional graph shows a straight line; inversely proportional graph shows a curve.
B. Directly proportional graph shows a curve; inversely proportional graph shows a straight line.
C. Both graphs show straight lines but have different slopes.
D. Both graphs show curves but have different shapes.

Answer 1

A graph representing data that is directly proportional shows a straight line, while a graph of data that is inversely proportional shows a curve. The correct option is A.

Step-by-step explanation:

A graph representing data that is directly proportional shows a straight line, while a graph of data that is inversely proportional shows a curve. In a directly proportional graph, as one variable increases, the other variable also increases at a consistent rate. On the other hand, in an inversely proportional graph, as one variable increases, the other variable decreases at a consistent rate.

For example, if we plot the relationship between distance and time for a moving object, a directly proportional graph would show a straight line passing through the origin, indicating that the object is moving at a constant speed. In contrast, an inversely proportional graph would show a curve, indicating that as the time increases, the distance covered by the object decreases at a consistent rate. Hence, A is the correct option.