Question
The constant of proportionality is the amount a relationship will change for each unit.
It is represented by the value of this ratio: k=yx
One of the ways a proportional relationship is identified is with an equation.
y=kx
The constant of proportionality (unit rate) is $2.25 per pound. The equation for this relationship is:
y = 2.25x
where y is the cost and x is the pound of oranges.
(8 points)
Determine the equation for each table and graph below.
The constant of proportionality is
and the equation for this relationship is
.
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The constant of proportionality is
and the equation for this relationship is
.
========================================
The constant of proportionality is
and the equation for this relationship is
.
========================================
The constant of proportionality is
and the equation for this relationship is
.
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It is represented by the value of this ratio: k=yx
One of the ways a proportional relationship is identified is with an equation.
y=kx
The constant of proportionality (unit rate) is $2.25 per pound. The equation for this relationship is:
y = 2.25x
where y is the cost and x is the pound of oranges.
(8 points)
Determine the equation for each table and graph below.
The constant of proportionality is
and the equation for this relationship is
.
========================================
The constant of proportionality is
and the equation for this relationship is
.
========================================
The constant of proportionality is
and the equation for this relationship is
.
========================================
The constant of proportionality is
and the equation for this relationship is
.
Skip to navigation
Answers
There are no human answers yet.
Answered by
GPT-4o mini
It looks like you're trying to determine equations for different proportional relationships based on given data in tables or graphs. However, without the specific tables or graphs to examine, I can't provide exact values or equations.
To help you understand how to derive the constant of proportionality and the corresponding equations from a table or graph, here’s a step-by-step approach:
1. **Identifying the Constant of Proportionality (k)**:
- Look at the ratio of \( y \) (dependent variable) to \( x \) (independent variable) at any given point.
- This ratio should remain constant across all points in a proportional relationship, meaning \( k = \frac{y}{x} \).
2. **Formulating the Equation**:
- Once you have determined \( k \), you can write the equation in the form \( y = kx \).
### Example
Let's go through a hypothetical example together:
**Suppose you have the following data:**
- When \( x = 1 \), \( y = 3 \)
- When \( x = 2 \), \( y = 6 \)
- When \( x = 3 \), \( y = 9 \)
1. Calculate the constant of proportionality:
- For \( x = 1 \), \( k = \frac{y}{x} = \frac{3}{1} = 3 \)
- For \( x = 2 \), \( k = \frac{y}{x} = \frac{6}{2} = 3 \)
- For \( x = 3 \), \( k = \frac{y}{x} = \frac{9}{3} = 3 \)
Since the ratio is constant, \( k = 3 \).
2. Write the equation:
- The equation representing this relationship is \( y = 3x \).
You would follow this same approach for each set of data you have.
If you can provide the specific tables or graphs, I would be happy to help you determine the constant of proportionality and the equations for each relationship!
To help you understand how to derive the constant of proportionality and the corresponding equations from a table or graph, here’s a step-by-step approach:
1. **Identifying the Constant of Proportionality (k)**:
- Look at the ratio of \( y \) (dependent variable) to \( x \) (independent variable) at any given point.
- This ratio should remain constant across all points in a proportional relationship, meaning \( k = \frac{y}{x} \).
2. **Formulating the Equation**:
- Once you have determined \( k \), you can write the equation in the form \( y = kx \).
### Example
Let's go through a hypothetical example together:
**Suppose you have the following data:**
- When \( x = 1 \), \( y = 3 \)
- When \( x = 2 \), \( y = 6 \)
- When \( x = 3 \), \( y = 9 \)
1. Calculate the constant of proportionality:
- For \( x = 1 \), \( k = \frac{y}{x} = \frac{3}{1} = 3 \)
- For \( x = 2 \), \( k = \frac{y}{x} = \frac{6}{2} = 3 \)
- For \( x = 3 \), \( k = \frac{y}{x} = \frac{9}{3} = 3 \)
Since the ratio is constant, \( k = 3 \).
2. Write the equation:
- The equation representing this relationship is \( y = 3x \).
You would follow this same approach for each set of data you have.
If you can provide the specific tables or graphs, I would be happy to help you determine the constant of proportionality and the equations for each relationship!
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