To determine if a graph correctly represents the equation \( y = \frac{1}{5}x \):
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Check the y-intercept: The equation \( y = \frac{1}{5}x \) has a y-intercept at (0, 0), which must be on the graph.
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Check the slope: The slope of the line is \( \frac{1}{5} \), meaning for every 5 units moved in the x-direction (to the right), the line moves 1 unit in the y-direction (upward).
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Check a specific point: For example, if the x-value is 1, then \( y = \frac{1}{5}(1) = \frac{1}{5} \). The point (1, 5) would not be on the graph of this line.
Based on this information, if the graph in question contains the ordered pair (0, 0), maintains a slope of \( \frac{1}{5} \), and does not incorrectly include points like (1, 5), then it could be deemed correct.
Among the provided options, the correct response should affirm that the graph has the appropriate slope of \( \frac{1}{5} \) and contains the origin (0, 0), while also indicating that the point (1, 5) should not be on the graph.
Thus, the correct response would be: "Yes, it is the correct graph because the ordered pair (0, 0) satisfies the equation and the slope \( m = \frac{\text{rise}}{\text{run}} = \frac{1}{5} \)."
If the graph does not reflect these features, choose accordingly regarding its incorrectness.
3 answers