To determine if the graph represents the equation \( y = \frac{1}{5} x \), we need to evaluate the given points and the slope.
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The equation \( y = \frac{1}{5} x \) implies that the slope \( m \) is \( \frac{1}{5} \). This means that for every 5 units you move in the x-direction, the y-value increases by 1 unit.
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The points given are (5, 1) and (0, 0).
- For the point (5, 1): \[ y = \frac{1}{5} \times 5 = 1 \quad \text{(this point satisfies the equation)} \]
- For the point (0, 0): \[ y = \frac{1}{5} \times 0 = 0 \quad \text{(this point also satisfies the equation)} \]
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The slope between the two points can be calculated as follows:
- Rise: \( 1 - 0 = 1 \)
- Run: \( 5 - 0 = 5 \)
- Slope \( m = \frac{\text{rise}}{\text{run}} = \frac{1}{5} \).
Since both points satisfy the equation \( y = \frac{1}{5} x \) and the calculated slope matches the expected slope from the equation, we can analyze the answer options:
- A states the slope is \( \frac{5}{1} \), which is incorrect.
- B states the slope is \( \frac{1}{5} \), which is correct, but it claims it does not represent the correct graph.
- C correctly states that both points satisfy the equation and that the slope is \( \frac{1}{5} \).
- D incorrectly states that (1, 5) is not a point on the graph, which is irrelevant to determining whether the graph is correct.
Given all of this, the best answer is:
C. Yes, It is the correct graph because the ordered pair (0, 0) satisfies the equation and the slope m = rise/run = 1/5.
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