To match the responses with the options provided, we can analyze each item:
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The constant of proportionality: This is the ratio of \(y\) to \(x\) when the graph represents a proportional relationship (a straight line through the origin). If the line's equation is \(y = \frac{1}{2}x\), then the constant of proportionality is \(\frac{1}{2}\).
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An equation that represents this graph: If the graph corresponds to a line with a constant slope of \(\frac{1}{2}\), the equation would be \(y = \frac{1}{2}x\).
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The y-intercept: The y-intercept is the point where the graph crosses the y-axis. If the graph goes through the origin (0, 0), then the y-intercept is (0, 0).
Now we can fill in the blanks:
- The constant of proportionality: 1/2
- An equation that represents this graph: y = 1/2x
- The y-intercept: (0, 0)
So, the answers are:
- The constant of proportionality: 1/2
- An equation that represents this graph: y = 1/2x
- The y-intercept: (0, 0)