To determine the correctness of the graph for the equation \( y = \frac{1}{5}x \), we can analyze the characteristics of this linear equation.
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Slope: The slope \( m \) of the line is \( \frac{1}{5} \), which means that for every 5 units you move horizontally (run), the line moves up 1 unit (rise).
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Y-Intercept: The graph of this equation will cross the y-axis at the origin (0, 0). This is the y-intercept.
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Ordered Pairs:
- The ordered pair (0, 0) is indeed on the graph, as substituting \( x = 0 \) gives \( y = 0 \).
- The ordered pair (1, 5) is not on the graph, because substituting \( x = 1 \) gives \( y = \frac{1}{5}(1) = \frac{1}{5} \), not 5.
Now let's look at the provided responses:
- "No, it is not the correct graph because the ordered pair (1, 5) is not a point on the graph of y = 1/5x." (This response is correct, as (1, 5) is not on the graph.)
- "Yes, it is the correct graph because the ordered pair (0, 0) satisfies the equation and the slope m = rise/run = 1/5." (This response is also correct.)
- The response mentioning that the slope is \( \frac{5}{1} \) is incorrect because the correct slope is \( \frac{1}{5} \).
Given that both the first response about the ordered pair (1, 5) is correct and the second response about the ordered pair (0, 0) and the slope being \( \frac{1}{5} \) is also correct, we can conclude the following:
- While there are multiple valid responses that can be considered correct, the most clear denial of the graph in question is the first response. The answer depends on the focus—whether you are emphasizing the incorrectness involving the specific ordered pair or confirming the correctness involving the origin and slope.
So, if required to choose the most appropriate response against the correctness of the graph, you would go with "No, it is not the correct graph because the ordered pair (1, 5) is not a point on the graph of y = 1/5x."