Ask questions, share knowledge, and connect with a vibrant community on IDNLearn.com. Our platform offers comprehensive and accurate responses to help you make informed decisions on any topic.
Sagot :
To determine which equation represents a proportional relationship with a constant of proportionality equal to 2, we need to evaluate each given equation and identify which one adheres to the definition of a proportional relationship.
A proportional relationship between two variables [tex]\( y \)[/tex] and [tex]\( x \)[/tex] can be expressed as:
[tex]\[ y = kx \][/tex]
where [tex]\( k \)[/tex] is the constant of proportionality. For this problem, we are given that the constant of proportionality, [tex]\( k \)[/tex], should be 2. Thus, we look for an equation of the form:
[tex]\[ y = 2x \][/tex]
Now, let's examine each of the given equations:
1. Equation: [tex]\( y = x + 2 \)[/tex]
- This is a linear equation, but it is not proportional because it has an additional constant term (the +2). In a proportional relationship, the graph must pass through the origin (0,0), and this equation does not satisfy that condition.
2. Equation: [tex]\( y = \frac{x}{2} \)[/tex]
- This equation represents a proportional relationship with a constant of proportionality of [tex]\( \frac{1}{2} \)[/tex]. Since our required constant is 2, this equation does not satisfy the condition.
3. Equation: [tex]\( y = 2x \)[/tex]
- This equation represents a proportional relationship where [tex]\( k = 2 \)[/tex]. The relationship is directly proportional, and the graph passes through the origin. This matches our requirement perfectly.
4. Equation: [tex]\( y = 2 \)[/tex]
- This is a constant function, not a relationship between [tex]\( y \)[/tex] and [tex]\( x \)[/tex] that changes with [tex]\( x \)[/tex]. It does not represent a proportional relationship.
Therefore, the correct equation that represents a proportional relationship with a constant of proportionality equal to 2 is:
[tex]\[ y = 2x \][/tex]
The index of the correct equation, given the provided options, is:
[tex]\[ \boxed{3} \][/tex]
A proportional relationship between two variables [tex]\( y \)[/tex] and [tex]\( x \)[/tex] can be expressed as:
[tex]\[ y = kx \][/tex]
where [tex]\( k \)[/tex] is the constant of proportionality. For this problem, we are given that the constant of proportionality, [tex]\( k \)[/tex], should be 2. Thus, we look for an equation of the form:
[tex]\[ y = 2x \][/tex]
Now, let's examine each of the given equations:
1. Equation: [tex]\( y = x + 2 \)[/tex]
- This is a linear equation, but it is not proportional because it has an additional constant term (the +2). In a proportional relationship, the graph must pass through the origin (0,0), and this equation does not satisfy that condition.
2. Equation: [tex]\( y = \frac{x}{2} \)[/tex]
- This equation represents a proportional relationship with a constant of proportionality of [tex]\( \frac{1}{2} \)[/tex]. Since our required constant is 2, this equation does not satisfy the condition.
3. Equation: [tex]\( y = 2x \)[/tex]
- This equation represents a proportional relationship where [tex]\( k = 2 \)[/tex]. The relationship is directly proportional, and the graph passes through the origin. This matches our requirement perfectly.
4. Equation: [tex]\( y = 2 \)[/tex]
- This is a constant function, not a relationship between [tex]\( y \)[/tex] and [tex]\( x \)[/tex] that changes with [tex]\( x \)[/tex]. It does not represent a proportional relationship.
Therefore, the correct equation that represents a proportional relationship with a constant of proportionality equal to 2 is:
[tex]\[ y = 2x \][/tex]
The index of the correct equation, given the provided options, is:
[tex]\[ \boxed{3} \][/tex]
We appreciate your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. Find clear answers at IDNLearn.com. Thanks for stopping by, and come back for more reliable solutions.