1. **State the problem:** We need to sketch the graph of the line given by the equation $y = -x + 4$. 2. **Recall the formula:** The equation is in slope-intercept form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. 3. **Identify slope and intercept:** Here, $m = -1$ and $b = 4$. This means the line crosses the y-axis at $(0,4)$ and for every 1 unit increase in $x$, $y$ decreases by 1. 4. **Find x-intercept:** Set $y=0$ to find the x-intercept: $$0 = -x + 4$$ $$x = 4$$ So the x-intercept is at $(4,0)$. 5. **Plot points:** Plot the points $(0,4)$ and $(4,0)$ on the coordinate plane. 6. **Draw the line:** Connect these points with a straight line extending in both directions. This line has a negative slope, so it goes downwards from left to right. **Final answer:** The graph is a straight line crossing the y-axis at 4 and the x-axis at 4, with slope $-1$.