To determine which point is a solution to the inequality \( y \leq 4x + 5 \), we need to check each point by substituting the x and y coordinates into the inequality.
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For the point \((-4, 0)\): \[ y = 0, \quad x = -4 \] \[ 0 \leq 4(-4) + 5 \implies 0 \leq -16 + 5 \implies 0 \leq -11 \quad \text{(false)} \]
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For the point \((0, -2)\): \[ y = -2, \quad x = 0 \] \[ -2 \leq 4(0) + 5 \implies -2 \leq 0 + 5 \implies -2 \leq 5 \quad \text{(true)} \]
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For the point \((-6, 4)\): \[ y = 4, \quad x = -6 \] \[ 4 \leq 4(-6) + 5 \implies 4 \leq -24 + 5 \implies 4 \leq -19 \quad \text{(false)} \]
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For the point \((0, 10)\): \[ y = 10, \quad x = 0 \] \[ 10 \leq 4(0) + 5 \implies 10 \leq 0 + 5 \implies 10 \leq 5 \quad \text{(false)} \]
The only point that satisfies the inequality \( y \leq 4x + 5 \) is \((0, -2)\).