It looks like you're working with a mathematical relationship represented by a linear equation and trying to identify various components of the equation. Let's break it down based on the information provided.
From your inline dropdown, let's fill in the queries step by step:
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Relationship: This would typically refer to the type of relationship that the equations represent. It can be either proportional or non-proportional. Given the equations, we need to identify that.
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Y-Intercept: The y-intercept is the value of \( y \) when \( x = 0 \). You can determine this from the equation:
- For \( y = 1x + 2 \), the y-intercept is \( 2 \).
- For \( y = \frac{1}{2}x + 1 \), the y-intercept is \( 1 \).
- For \( y = 2x + 1 \), the y-intercept is \( 1 \).
- For \( y = \frac{1}{2}x \), the y-intercept is \( 0 \).
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Slope: The slope is the coefficient of \( x \) in the equations:
- For \( y = 1x + 2 \), the slope is \( 1 \).
- For \( y = \frac{1}{2}x + 1 \), the slope is \( \frac{1}{2} \).
- For \( y = 2x + 1 \), the slope is \( 2 \).
- For \( y = \frac{1}{2}x \), the slope is \( \frac{1}{2} \).
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Equation of the line in slope-intercept form: This is the original form, which is typically given as \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
Using some of the provided information, here’s an example of how to fill in a specific case:
- Relationship: Non-proportional (since at least one y-intercept is not zero).
- Y-intercept: If we use \( y = 1x + 2 \), the y-intercept is \( 2 \).
- Slope: Using \( y = 1x + 2 \), the slope is \( 1 \).
- Equation of the line: Using the equation \( y = 1x + 2 \).
If desired, please specify which equation you would like to analyze, and I can provide tailored answers accordingly!