\begin{tabular}{|c|c} Determine whether \( (8,13) \) is a solution of \( y=5 x+11 \). & \( \begin{array}{l}\text { Is the point }(8,13) \text { a solution of the equation } \\ y=5 x+11 \text { ? }\end{array} \) \\ No \\ O & Yes \end{tabular}
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The Deep Dive
To determine if the point \( (8, 13) \) is a solution to the equation \( y = 5x + 11 \), we need to substitute \( x = 8 \) into the equation and see if we get \( y = 13 \). Calculating: \[ y = 5(8) + 11 = 40 + 11 = 51 \] Since \( y \) equals \( 51 \), which does not match \( 13 \), the point \( (8, 13) \) is not a solution to the equation. If you ever need to check if a point is a solution to an equation, substitute the x-value into the equation and see if it equals the y-value of the point. A classic mistake is assuming a point is a solution without verifying it against the equation. So, always double-check those calculations!
