y and x are in a proportional relationship. y = 100 when x = 50. Write an equation that represents this relationship.
Understand the Problem
The question is asking to represent a proportional relationship between y and x given that y equals 100 when x equals 50. We need to derive the equation that reflects this relationship based on the provided options.
Answer
The equation that represents the relationship is $y = 2x$.
Answer for screen readers
The equation that represents the relationship is $y = 2x$.
Steps to Solve
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Identify the proportional relationship In a proportional relationship, the formula is generally of the form $y = kx$, where $k$ is a constant. Given that $y = 100$ when $x = 50$, we can find $k$.
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Substitute values to find k We substitute the known values into the formula: $$100 = k(50)$$
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Solve for k To isolate $k$, divide both sides by 50: $$k = \frac{100}{50} = 2$$
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Write the equation Now that we have determined $k$, we can write the equation as: $$y = 2x$$
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Select the correct option Looking at the options provided:
- $y = 3x$
- $y = 10x$
- $y = 5x$
- $y = 2x$
The correct option is $y = 2x$.
The equation that represents the relationship is $y = 2x$.
More Information
In a proportional relationship, the ratio of $y$ to $x$ remains constant. Here, $k = 2$ indicates that for every unit increase in $x$, $y$ increases by 2 units.
Tips
- Misidentifying the proportionality constant $k$. Always ensure to solve for $k$ accurately using the given values.
- Forgetting to match the form $y = kx$ when expressing the relationship.
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