To find the graph that matches the linear equation \( 6x + y = -4 \), we can rearrange the equation into slope-intercept form (\( y = mx + b \)).
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Start with the original equation: \[ 6x + y = -4 \]
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Subtract \( 6x \) from both sides: \[ y = -6x - 4 \]
From this equation, we can see that:
- The slope (\( m \)) is \(-6\).
- The y-intercept (\( b \)) is \(-4\).
Characteristics of the graph:
- The line will have a steep negative slope and will decrease sharply as \( x \) increases.
- It will cross the y-axis at the point (0, -4).
To choose the correct graph:
- Look for a line that slopes downwards from left to right.
- Verify that the line crosses the y-axis at the point (0, -4).
Without visual options, I cannot select a specific graph. However, you should use these characteristics to identify the correct graph from the options you have.
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