To determine if the point (4, 7) is a solution to the inequality \( y < -\frac{3}{4}x - 5 \), we can substitute \( x = 4 \) and \( y = 7 \) into the inequality.
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Substitute \( x = 4 \) into the inequality: \[ y < -\frac{3}{4}(4) - 5 \]
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Calculate the right side: \[ -\frac{3}{4}(4) = -3 \] So the inequality becomes: \[ y < -3 - 5 \] Simplifying further gives: \[ y < -8 \]
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Now substitute \( y = 7 \) into the inequality: \[ 7 < -8 \]
This statement is false. Therefore, (4, 7) is not a solution to the inequality \( y < -\frac{3}{4}x - 5 \).
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