To determine whether the graph in question accurately represents the equation \( y = 15x \), we need to consider a few key points:
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The Slope: The slope \( m \) of the equation \( y = 15x \) is 15, which means for every 1 unit increase in \( x \), \( y \) increases by 15 units. Thus, the slope in rise/run terms is \( 15/1 \).
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The Y-Intercept: The graph should pass through the origin (0, 0) since when \( x = 0 \), \( y \) should also be 0.
Evaluating the responses given:
- The correct graph must have a slope of \( 15 \), not \( 1/5 \) or any other fraction.
- The ordered pair (0, 0) must satisfy the equation correctly since it is the y-intercept.
Based on this logic:
- The response option saying "Yes, it is the correct graph because the ordered pair (0, 0) satisfies the equation and the slope \( m = \frac{rise}{run} = 15 \)" would be the correct choice if true.
- Options stating the slope equals \( \frac{1}{5} \) or any incorrect other value, or suggesting that the ordered pair (1, 5) is not valid for the equation, would be incorrect.
Therefore, if the graph has a slope of \( 15 \) and passes through (0, 0), the response would be "Yes, it is the correct graph because the ordered pair (0, 0) satisfies the equation and the slope \( m = \frac{rise}{run} = 15 \)." If another option provides incorrect slope values or points, it could be marked as incorrect.
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