1. The problem is to sketch the lines for the equations: $$1)\ 4x + 3y = 11$$ $$2)\ 2x + y = 5$$ 2. To graph a line, we find its intercepts by setting $x=0$ to find the $y$-intercept and $y=0$ to find the $x$-intercept. 3. For the first line $4x + 3y = 11$: - Set $x=0$: $$4(0) + 3y = 11 \Rightarrow 3y = 11 \Rightarrow y = \frac{11}{3} \approx 3.67$$ - Set $y=0$: $$4x + 3(0) = 11 \Rightarrow 4x = 11 \Rightarrow x = \frac{11}{4} = 2.75$$ 4. For the second line $2x + y = 5$: - Set $x=0$: $$2(0) + y = 5 \Rightarrow y = 5$$ - Set $y=0$: $$2x + 0 = 5 \Rightarrow 2x = 5 \Rightarrow x = \frac{5}{2} = 2.5$$ 5. These intercepts give points to plot: - First line: $(0, 3.67)$ and $(2.75, 0)$ - Second line: $(0, 5)$ and $(2.5, 0)$ 6. Draw straight lines through these points to sketch the graphs. Final answer: The lines pass through the points calculated above, matching the given graph description.