\( \left. \begin{array} { l } { 6 x - 7 y = - 18 } \\ \hline ( - 5,3 ) \\ \hline ( 4,0 ) \\ \hline ( 1 , - 5 ) \\ \hline \text { Submit } \\ \hline \end{array} \right. \)

To determine which of the given points satisfies the equation \(6x - 7y = -18\), we can plug each point into the equation and see if it holds true: 1. For the point \((-5, 3)\): \[ 6(-5) - 7(3) = -30 - 21 = -51 \quad (\text{Not a solution}) \] 2. For the point \((4, 0)\): \[ 6(4) - 7(0) = 24 - 0 = 24 \quad (\text{Not a solution}) \] 3. For the point \((1, -5)\): \[ 6(1) - 7(-5) = 6 + 35 = 41 \quad (\text{Not a solution}) \] None of the provided points satisfy the equation. However, if you're curious about why equations like this are important, they often form the backbone of understanding linear relationships, which can be applied in numerous fields, ranging from physics to economics. Linear equations help us predict outcomes based on certain inputs, making them invaluable tools in data analysis! To avoid common mistakes when working with linear equations, always double-check by substituting your x and y values back into the original equation. It’s a simple step that can save you from frustration later on. Plus, writing down each calculated step can clarify the process and help catch any errors!