To determine the equation for the proportional relationship represented by the graph, we need to identify whether the graph depicts a line that passes through the origin or one that has a y-intercept different from zero.
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Proportional Relationships: These are depicted by equations of the form \( y = kx \) (where \( k \) is a constant). The graph of a proportional relationship will go through the point (0,0) and has no y-intercept (other than zero).
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Non-Proportional Relationships: These will typically have a y-intercept that is not zero, represented by equations of the form \( y = kx + b \) (where \( b \neq 0\)).
Given the options:
- \( y = 1x \) (which simplifies to \( y = x \)) is proportional.
- \( y = 5x \) is also proportional.
- \( y = 5x + 5 \) is not proportional (since it has a y-intercept of 5).
- \( y = 1x + 5 \) is also not proportional (since it has a y-intercept of 5).
If the graph shows a linear relationship passing through the origin, then both \( y = x \) and \( y = 5x \) are correct. Otherwise, if it does not pass through the origin, the other equations represent a relationship with a non-zero intercept.
Please refer to the specific graph you're analyzing to determine the correct equation. If you know whether the graph goes through (0,0) or not, you can confidently pick the appropriate equation from the options given.
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