To determine if the quantities x and y described by the equation \( y = 34x - 5 \) are in a proportional relationship, we need to consider the characteristics of proportional relationships.
A proportional relationship has the following features:
- The equation takes the form \( y = kx \), where \( k \) is a constant (the constant of proportionality).
- The graph of a proportional relationship is a straight line that passes through the origin (0,0).
- The ratio \( y/x \) is constant for any point on the line.
Looking at the given equation \( y = 34x - 5 \):
- It is not in the form \( y = kx \) because of the "-5" term.
- The graph of this equation is a straight line because it is a linear equation, but it does not pass through the origin because when \( x = 0 \), \( y = -5 \).
- Therefore, the ratio \( y/x \) will not be constant, as it will vary depending on the value of \( x \).
Based on this analysis, the correct response is:
No, because the graph of the equation does not pass through the origin and the ratio of \( y/x \) is not equivalent for each point on the line.
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