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Does the equation y ż represent a proportional relationship?

a) No, because its graph does not pass through the origin.
b) No, because it is not in the form y ku.
c) Yes, because the coefficient of ż is positive.
d) Yes, because its graph is a line that passes through the origin.

User StuBez
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1 Answer

5 votes

Final answer:

The equation y = ż represents a proportional relationship because it can be expressed in the form y = kx, where k is implicitly 1, and its graph would be a straight line passing through the origin, satisfying the criteria for a proportional relationship.

Step-by-step explanation:

The question asks whether the equation y = ż represents a proportional relationship. A proportional relationship is defined as a relationship between two quantities where they maintain a constant ratio or rate. In mathematical terms, a proportional relationship can be represented by an equation of the form y = kx, where k is the proportionality constant. Furthermore, the graph of a proportional relationship must be a straight line that passes through the origin (0,0).

To determine if the equation y = ż represents a proportional relationship, we must consider if it can be rewritten in the form y = kx and if its graph passes through the origin. Since the symbol ż can be considered a variable, we assume it represents x in the proportional form. The presence of only ż and its coefficient being 1 (implicit) means that the equation can be expressed as y = 1x.

The correct answer to whether the equation represents a proportional relationship is yes, because its graph is a straight line that passes through the origin, matching option (d).

User Nitish Parkar
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