The equation you've provided is a linear equation in two variables, \( x \) and \( y \). To analyze or manipulate it, we can convert it into different forms such as the slope-intercept form (y = mx + b) or solve for one variable in terms of the other.
Here’s how to put it in slope-intercept form:
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Start with the original equation: \[ 6x - 3y = 30 \]
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Solve for \( y \):
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First, isolate the term involving \( y \): \[ -3y = -6x + 30 \]
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Next, divide all terms by -3 to solve for \( y \): \[ y = 2x - 10 \]
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Now it's in slope-intercept form, where the slope \( m \) is 2 and the y-intercept \( b \) is -10.
If you want to express \( y \) in terms of \( x \):
From the slope-intercept form we already derived: \[ y = 2x - 10 \]
Alternatively, you can solve for \( x \) in terms of \( y \):
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Start with the original equation: \[ 6x - 3y = 30 \]
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Solve for \( x \):
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First, isolate the term involving \( x \): \[ 6x = 3y + 30 \]
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Next, divide all terms by 6: \[ x = \frac{1}{2}y + 5 \]
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Summary:
- Slope-intercept form: \( y = 2x - 10 \)
- \( x \) in terms of \( y \): \( x = \frac{1}{2}y + 5 \)
Let me know if you need further assistance or if you would like to graph it or find specific points!