Determine whether the graphs of the given pair of lines are parallel. \[ \begin{array}{l}x+2=y \\ y-x=-3\end{array} \] Note that two nonvertical lines are parallel if they have \( \square y \) slope(s) and

To determine whether the given pair of lines are parallel, we'll analyze their slopes. Two non-vertical lines are parallel if they have the **same** slope but different y-intercepts. Let's rewrite each equation in the slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. 1. **First Equation:** \[ x + 2 = y \quad \Rightarrow \quad y = x + 2 \] - **Slope (\( m \))**: 1 - **Y-intercept (\( b \))**: 2 2. **Second Equation:** \[ y - x = -3 \quad \Rightarrow \quad y = x - 3 \] - **Slope (\( m \))**: 1 - **Y-intercept (\( b \))**: -3 **Comparison:** - Both lines have the **same slope** of 1. - They have **different y-intercepts** (2 and -3). Since both lines have identical slopes but different y-intercepts, they do not intersect and are therefore **parallel**. **Conclusion:** Yes, the two lines are parallel because both have the same slope of 1.