To find the equation of the boundary line for the inequality \(6x - 3y > 15\), we first convert the inequality into an equation by replacing the inequality sign with an equality. Thus, we have:
\[ 6x - 3y = 15 \]
Next, we can rewrite this equation in slope-intercept form (\(y = mx + b\)) by isolating \(y\):
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Start with the original equation: \[ 6x - 3y = 15 \]
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Subtract \(6x\) from both sides: \[ -3y = -6x + 15 \]
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Divide each term by \(-3\) (remember to flip the inequality sign when dividing by a negative): \[ y = 2x - 5 \]
So, the equation of the boundary line is:
\[ y = 2x - 5 \]
This line represents the boundary for the inequality \(6x - 3y > 15\). The solution to the inequality will lie above this line (since the inequality is greater than).