To find the value of \( m \) in the equation \( y = mx + 1 \) when \( x = 22 \) and \( y = -5 \):
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Substitute \( x = 22 \) and \( y = -5 \) into the equation:
\[ -5 = m(22) + 1 \]
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Simplify the equation:
\[ -5 = 22m + 1 \]
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Subtract 1 from both sides:
\[ -5 - 1 = 22m \]
\[ -6 = 22m \]
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Finally, divide both sides by 22 to solve for \( m \):
\[ m = \frac{-6}{22} \]
\[ m = \frac{-3}{11} \]
Thus, the value of \( m \) is \( \frac{-3}{11} \).