Bot GPT 4-o mini To determine which graph matches the equation \(3x + y = 6\), we can first rearrange the equation into slope-intercept form ( \(y = mx + b\) ), which makes it easier to identify the slope and y-intercept.
Starting with the original equation:
\[ 3x + y = 6 \]
Now, isolate \(y\):
\[ y = -3x + 6 \]
From the equation \(y = -3x + 6\):
- The slope \(m\) is \(-3\), which means the line decreases as \(x\) increases.
- The y-intercept \(b\) is \(6\), meaning the line crosses the y-axis at the point \((0, 6)\).
Steps to identify the graph:
- Check the y-intercept: Find where the line crosses the y-axis; it should be at \( (0, 6) \).
- Check the slope: From the y-intercept, move down 3 units and to the right 1 unit to plot another point.
- Determine the general direction: The line should slope downward from left to right due to the negative slope.
You can now compare these characteristics to the provided graphs to identify the correct one. Look for a line that starts at \( (0, 6) \) and descends towards the right.
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