1. **State the problem:** We need to graph the two linear equations $y = 4x - 1$ and $y = -x + 4$. 2. **Recall the slope-intercept form:** The general form of a linear equation is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. 3. **Analyze the first equation $y = 4x - 1$:** - Slope $m = 4$ means the line rises 4 units for every 1 unit it moves to the right. - Y-intercept $b = -1$ means the line crosses the y-axis at $(0, -1)$. 4. **Analyze the second equation $y = -x + 4$:** - Slope $m = -1$ means the line falls 1 unit for every 1 unit it moves to the right. - Y-intercept $b = 4$ means the line crosses the y-axis at $(0, 4)$. 5. **Find x-intercepts by setting $y=0$:** - For $y = 4x - 1$, set $0 = 4x - 1$ which gives: $$ 4x = 1 \\ \cancel{4}x = \frac{1}{\cancel{4}} \\ x = \frac{1}{4} $$ - For $y = -x + 4$, set $0 = -x + 4$ which gives: $$ -x = -4 \\ \cancel{-}x = \frac{-4}{\cancel{-}} \\ x = 4 $$ 6. **Summary of key points:** - Line 1 passes through $(0, -1)$ and $(\frac{1}{4}, 0)$. - Line 2 passes through $(0, 4)$ and $(4, 0)$. 7. **Plot these points and draw straight lines through them to graph the equations.** This completes the graphing of the two lines.