Question
A graph is a straight line through the point (0, 5). Can the graph represent a proportional relationship? Explain.
Yes; the constant of proportionality is 5.
Yes; the equation of the line can be written in the form y = kx, where k = 5.
Yes; the graph is a straight line that crosses the y-axis at (0, 5).
No; the graph of a proportional relationship must pass through (0, 0).
Yes; the constant of proportionality is 5.
Yes; the equation of the line can be written in the form y = kx, where k = 5.
Yes; the graph is a straight line that crosses the y-axis at (0, 5).
No; the graph of a proportional relationship must pass through (0, 0).
Answers
GPT-4o mini
No; the graph of a proportional relationship must pass through (0, 0).
A proportional relationship is defined as one in which the ratio of the two quantities remains constant, and it is typically represented by a line that passes through the origin (0, 0). In this case, the graph passes through (0, 5), not (0, 0), indicating that while there may be a consistent relationship, it is not proportional since a proportional relationship cannot have a y-intercept other than zero. Thus, the correct answer is that it cannot represent a proportional relationship.
A proportional relationship is defined as one in which the ratio of the two quantities remains constant, and it is typically represented by a line that passes through the origin (0, 0). In this case, the graph passes through (0, 5), not (0, 0), indicating that while there may be a consistent relationship, it is not proportional since a proportional relationship cannot have a y-intercept other than zero. Thus, the correct answer is that it cannot represent a proportional relationship.
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