The equation you've provided, \( x + 6y = -1 \), is a linear equation in two variables, \( x \) and \( y \). If you want to solve for one variable in terms of the other, here is how you can do it:
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Solve for \( x \) in terms of \( y \): \[ x = -1 - 6y \]
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Solve for \( y \) in terms of \( x \): \[ 6y = -1 - x \quad \Rightarrow \quad y = \frac{-1 - x}{6} \]
If you're looking for a graph, this equation can be represented as a straight line in the Cartesian plane. You can find specific points by plugging in different values for \( y \) (or \( x \)).
For example:
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If \( y = 0 \): \[ x + 6(0) = -1 \quad \Rightarrow \quad x = -1 \quad \Rightarrow \quad (-1, 0) \]
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If \( y = 1 \): \[ x + 6(1) = -1 \quad \Rightarrow \quad x + 6 = -1 \quad \Rightarrow \quad x = -7 \quad \Rightarrow \quad (-7, 1) \]
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If \( x = 0 \): \[ 0 + 6y = -1 \quad \Rightarrow \quad 6y = -1 \quad \Rightarrow \quad y = -\frac{1}{6} \quad \Rightarrow \quad (0, -\frac{1}{6}) \]
You can plot these points and draw the line to visualize the equation. If you have a specific request regarding this equation, such as finding intersections with another line, graphing it, or analyzing it in some other way, please let me know!