To determine which graph corresponds to the equation \( 3x + 5y = 2 \), we need to find the slope and y-intercept of the line.
First, we can rearrange the equation into slope-intercept form (\( y = mx + b \)):
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Start with the original equation: \[ 3x + 5y = 2 \]
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Isolate \( y \) on one side: \[ 5y = -3x + 2 \]
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Divide every term by 5: \[ y = -\frac{3}{5}x + \frac{2}{5} \]
From this, we see that the slope \( m \) is \( -\frac{3}{5} \) and the y-intercept \( b \) is \( \frac{2}{5} \).
Now, let's analyze the given options:
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First option: A line passing through (negative 5, negative 4), (0, negative 1), and (3, 1).
- Calculate the slope between the points (0, -1) and (3, 1): \[ m = \frac{1 - (-1)}{3 - 0} = \frac{2}{3} \]
- This slope does not match \( -\frac{3}{5} \).
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Second option: A line passing through (negative 1, 1) and (4, negative 2).
- Calculate the slope: \[ m = \frac{-2 - 1}{4 - (-1)} = \frac{-3}{5} \]
- The slope matches \( -\frac{3}{5} \).
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Third option: A line passing through (0, 1) and (3, negative 4).
- Calculate the slope: \[ m = \frac{-4 - 1}{3 - 0} = \frac{-5}{3} \]
- This slope does not match \( -\frac{3}{5} \).
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Fourth option: A line passing through (0, negative 2) and (1, 0).
- Calculate the slope: \[ m = \frac{0 - (-2)}{1 - 0} = \frac{2}{1} = 2 \]
- This slope does not match \( -\frac{3}{5} \).
Conclusion
The only option that has a slope of \( -\frac{3}{5} \) is the second option, which shows the graph of the equation \( 3x + 5y = 2 \).
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