1. **State the problem:** We have two equations: $x = a + b$ and $y = a - b$, with $a = 3$. We want to understand the relationship between $x$ and $y$ and how they relate to the points forming a right-angled triangle. 2. **Substitute the known value:** Since $a = 3$, substitute into the equations: $$x = 3 + b$$ $$y = 3 - b$$ 3. **Express $b$ in terms of $x$:** From $x = 3 + b$, we get $$b = x - 3$$ 4. **Substitute $b$ into $y$:** $$y = 3 - (x - 3) = 3 - x + 3 = 6 - x$$ 5. **Final relationship:** The equation relating $x$ and $y$ is $$y = 6 - x$$ 6. **Interpretation:** This is a straight line with intercepts at $x=6$ (where $y=0$) and $y=6$ (where $x=0$). The points $A$, $B$, and $C$ form a right-angled triangle with the base along the $x$-axis from $A$ to $B$, height along the $y$-axis from $B$ to $C$, and hypotenuse from $A$ to $C$. This matches the description of the triangle located in the bottom-right corner of the image. **Answer:** The relationship between $x$ and $y$ is $$y = 6 - x$$