To determine if the graph is correct for the equation \( y = 15x \), we need to evaluate a few key characteristics:
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Check the y-intercept: The equation \( y = 15x \) has a y-intercept at (0,0). This means that the graph must pass through the origin.
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Check the slope: The slope \( m \) of the line is 15, which means that for every 1 unit increase in \( x \), \( y \) should increase by 15 units.
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Check ordered pairs: You can also evaluate other points on the graph. For example, if \( x = 1 \), then \( y = 15(1) = 15 \). Thus, the point (1, 15) should be on the graph.
Now we can evaluate the responses given:
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The first response states that the slope is \( \frac{\text{rise}}{\text{run}} = 15 \) and that the point (0, 0) satisfies the equation, which is accurate if the graph does pass through the origin and has the correct slope.
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The second response claims that the slope is \( \frac{1}{5} \), which is incorrect for the equation \( y = 15x \).
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The third and fourth responses also incorrectly quote the slope \( \frac{1}{5} \) for \( y = 15x \), so they are incorrect.
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The last two responses seem to have a misunderstanding regarding the points listed. The equation \( y = 15x \) should have (1, 15) instead of (1, 5).
Based on this evaluation, the correct response would be:
No, it is not the correct graph because the ordered pair (1, 5) is not a point on the graph of \( y = 15x \).
This response reflects the fact that the slope is not accurate and misrepresented by the graph.
11 answers