1. **State the problem:** We have a line $n$ passing through points $(-2,5)$ and $(1,-1)$. A. Find the equation of line $n$ in the form $ax + by = c$ where $a,b,c$ are integers. B. Find the area of triangle $ORS$ formed by the origin $O(0,0)$ and the points $R$ and $S$ where line $n$ meets the x-axis and y-axis respectively. 2. **Find the slope of line $n$:** The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. $$m = \frac{-1 - 5}{1 - (-2)} = \frac{-6}{3} = -2$$ 3. **Use point-slope form to find the equation:** Using point $(1,-1)$: $$y - (-1) = -2(x - 1)$$ $$y + 1 = -2x + 2$$ $$y = -2x + 1$$ 4. **Convert to standard form $ax + by = c$ with integers:** $$y = -2x + 1$$ $$2x + y = 1$$ So, the equation is $2x + y = 1$. 5. **Find intercepts:** - For x-intercept $R$, set $y=0$: $$2x + 0 = 1 \Rightarrow x = \frac{1}{2}$$ So, $R = \left(\frac{1}{2}, 0\right)$. - For y-intercept $S$, set $x=0$: $$0 + y = 1 \Rightarrow y = 1$$ So, $S = (0,1)$. 6. **Calculate area of triangle $ORS$:** Triangle $ORS$ has vertices $O(0,0)$, $R\left(\frac{1}{2},0\right)$, and $S(0,1)$. Area formula for triangle with base and height on axes: $$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$$ Base = length $OR = \frac{1}{2}$, Height = length $OS = 1$. $$\text{Area} = \frac{1}{2} \times \frac{1}{2} \times 1 = \frac{1}{4}$$ **Final answers:** A. Equation of line $n$ is $2x + y = 1$. B. Area of triangle $ORS$ is $\frac{1}{4}$ square units.