Is \( (-1,-3) \) a solution to the linear equation \( y=x-2 \)

To determine if the point \((-1, -3)\) is a solution to the equation \(y = x - 2\), we can substitute \(x = -1\) into the equation. Plugging in, we have: \[ y = -1 - 2 = -3 \] Since the \(y\)-value obtained from the equation (-3) matches the \(y\)-value of the point (-3), we can conclude that \((-1, -3)\) is indeed a solution to the linear equation \(y = x - 2\). Now, let's explore some engaging insights! Did you know that the concept of linear equations can be traced back to ancient civilizations? Babylonians used geometric methods to solve linear equations over 4,000 years ago, paving the way for modern algebra. If you're planning to graph this equation, remember that the slope-intercept form is super useful! Always double-check your slope (in this case, the coefficient of \(x\) is 1) and y-intercept (which is -2 for this equation). A common mistake is miscalculating these values, so watch those signs closely!