A direct relationship between two variables means that as one variable increases, the other variable also increases. Similarly, when one decreases, the other decreases as well.
Example: The relationship between the number of hours worked and the amount of money earned. As the number of hours worked increases, the amount of money earned also increases. If you graph this relationship, it would form an upward-sloping line.
Let's say you're paid $10 per hour:
Hours worked (Variable X) Money earned (Variable Y)
0 $0
1 $10
2 $20
3 $30
As you can see, when the hours worked increase by 1, the money earned also increases by $10, showing a direct relationship.
Inverse Relationship:
An inverse relationship between two variables means that as one variable increases, the other variable decreases, or vice versa.
Example: The relationship between the speed of a car and the time taken to reach a destination. As the speed of the car increases, the time taken to reach the destination decreases. If you graph this relationship, it would form a downward-sloping curve.
Let's assume a constant distance of 100 miles:
Speed of the car (Variable X) Time taken to reach destination (Variable Y)
50 mph 2 hours
75 mph 1.33 hours (approx.)
100 mph 1 hour
125 mph 0.8 hours (approx.)
Here, as the speed of the car increases, the time taken to reach the destination decreases, displaying an inverse relationship.
These examples illustrate the concepts of direct and inverse relationships between variables in mathematics.
Answers & Comments
Answer:
A direct relationship between two variables means that as one variable increases, the other variable also increases. Similarly, when one decreases, the other decreases as well.
Example: The relationship between the number of hours worked and the amount of money earned. As the number of hours worked increases, the amount of money earned also increases. If you graph this relationship, it would form an upward-sloping line.
Let's say you're paid $10 per hour:
Hours worked (Variable X) Money earned (Variable Y)
0 $0
1 $10
2 $20
3 $30
As you can see, when the hours worked increase by 1, the money earned also increases by $10, showing a direct relationship.
Inverse Relationship:
An inverse relationship between two variables means that as one variable increases, the other variable decreases, or vice versa.
Example: The relationship between the speed of a car and the time taken to reach a destination. As the speed of the car increases, the time taken to reach the destination decreases. If you graph this relationship, it would form a downward-sloping curve.
Let's assume a constant distance of 100 miles:
Speed of the car (Variable X) Time taken to reach destination (Variable Y)
50 mph 2 hours
75 mph 1.33 hours (approx.)
100 mph 1 hour
125 mph 0.8 hours (approx.)
Here, as the speed of the car increases, the time taken to reach the destination decreases, displaying an inverse relationship.
These examples illustrate the concepts of direct and inverse relationships between variables in mathematics.