To determine if the point (-8, -2) is a solution to the inequality \( y < -\frac{3}{4}x - 5 \), we can substitute \( x = -8 \) and \( y = -2 \) into the inequality.
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Substitute \( x = -8 \) into the equation: \[ y < -\frac{3}{4}(-8) - 5 \]
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Calculate \(-\frac{3}{4}(-8)\): \[ -\frac{3}{4}(-8) = \frac{3 \cdot 8}{4} = \frac{24}{4} = 6 \]
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Now substitute this back into the inequality: \[ y < 6 - 5 \]
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Simplify: \[ y < 1 \]
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Now substitute \( y = -2 \): \[ -2 < 1 \]
This statement is true.
Since substituting (-8, -2) into the inequality results in a true statement, we conclude that (-8, -2) is a solution to the inequality \( y < -\frac{3}{4}x - 5 \).