To determine the correct graph for the equations \( -3x - y = 3 \) and \( y = -3x + 4 \), we first need to convert the first equation into the slope-intercept form (y = mx + b).
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Start with the equation: \[ -3x - y = 3 \]
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Rearrange it: \[ -y = 3 + 3x \] \[ y = -3x - 3 \]
Now we have both equations:
- \( y = -3x - 3 \) (from the first equation)
- \( y = -3x + 4 \) (from the second equation)
Next, we can analyze the slopes of both lines:
- The slope of the first line \((-3x - 3)\) is \(-3\).
- The slope of the second line \((-3x + 4)\) is also \(-3\).
Since both lines have the same slope, they are parallel and will never intersect.
Therefore, the correct response would be: Two parallel lines are graphed across a coordinate plane. One line is dotted while the other is solid.