1. **Stating the problem:** Plot the graphs of the linear equations: a) $2x - y = -4$ b) $3x - y = 2$ c) $y + 3x = 1$ d) $2y - x = 2$ e) $x - y = 3$ f) $x + y = 5$ 2. **Formula and rules:** To plot each line, find the intercepts by setting $x=0$ to find $y$-intercept and $y=0$ to find $x$-intercept. 3. **Plotting each line:** **a) $2x - y = -4$** - Set $x=0$: $2(0) - y = -4 \Rightarrow -y = -4 \Rightarrow y=4$ - Set $y=0$: $2x - 0 = -4 \Rightarrow 2x = -4 \Rightarrow x = -2$ **b) $3x - y = 2$** - Set $x=0$: $3(0) - y = 2 \Rightarrow -y = 2 \Rightarrow y = -2$ - Set $y=0$: $3x - 0 = 2 \Rightarrow 3x = 2 \Rightarrow x = \frac{2}{3}$ **c) $y + 3x = 1$** - Set $x=0$: $y + 3(0) = 1 \Rightarrow y = 1$ - Set $y=0$: $0 + 3x = 1 \Rightarrow 3x = 1 \Rightarrow x = \frac{1}{3}$ **d) $2y - x = 2$** - Set $x=0$: $2y - 0 = 2 \Rightarrow 2y = 2 \Rightarrow y = 1$ - Set $y=0$: $2(0) - x = 2 \Rightarrow -x = 2 \Rightarrow x = -2$ **e) $x - y = 3$** - Set $x=0$: $0 - y = 3 \Rightarrow -y = 3 \Rightarrow y = -3$ - Set $y=0$: $x - 0 = 3 \Rightarrow x = 3$ **f) $x + y = 5$** - Set $x=0$: $0 + y = 5 \Rightarrow y = 5$ - Set $y=0$: $x + 0 = 5 \Rightarrow x = 5$ 4. **Summary of intercepts for plotting:** | Equation | $x$-intercept | $y$-intercept | |---|---|---| | a) $2x - y = -4$ | $-2$ | $4$ | | b) $3x - y = 2$ | $\frac{2}{3}$ | $-2$ | | c) $y + 3x = 1$ | $\frac{1}{3}$ | $1$ | | d) $2y - x = 2$ | $-2$ | $1$ | | e) $x - y = 3$ | $3$ | $-3$ | | f) $x + y = 5$ | $5$ | $5$ | 5. **Explanation:** Each line can be drawn by plotting these intercept points on the coordinate plane and connecting them with a straight line. This completes the plotting exercise for the given equations.