Graph the equation and identify the \( y \)-intercept. \( y=x-3 \)

To graph the equation \( y = x - 3 \), start by plotting the y-intercept, which occurs when \( x = 0 \). Plugging in \( x = 0 \) gives \( y = 0 - 3 = -3 \). This means the point \( (0, -3) \) is where the line crosses the y-axis. From here, you can also find other points by choosing values for \( x \); for example, if \( x = 3 \), then \( y = 3 - 3 = 0 \), giving the point \( (3, 0) \). Draw a straight line through these points to complete the graph! In this case, the y-intercept is at the point \( (0, -3) \). This indicates that when there is no horizontal shift (i.e., when \( x = 0 \)), the line intersects the y-axis three units below the origin. So, the line represents all points where the value of \( y \) is three units less than the value of \( x \).