1. **Stating the problem:** Determine the coordinates of the point B, which is the intersection of the graphs of two functions: $f$, a function of inverse proportionality, and $g$, an affine function. 2. **Given information:** - Function $f$ is of inverse proportionality: $xy = 15$ or $y = \frac{15}{x}$. - Function $g$ is affine, passing through points $(2,0)$ and $(0,-2)$. 3. **Find the equation of $g$:** - Slope $a = \frac{0 - (-2)}{2 - 0} = \frac{2}{2} = 1$. - Intercept $b = -2$. - So, $g(x) = x - 2$. 4. **Find the intersection point $B$:** - At intersection, $f(x) = g(x)$, so: $$\frac{15}{x} = x - 2$$ 5. **Solve for $x$:** - Multiply both sides by $x$ ($x \neq 0$): $$15 = x(x - 2) = x^2 - 2x$$ - Rearrange: $$x^2 - 2x - 15 = 0$$ 6. **Solve quadratic equation:** - Use quadratic formula: $$x = \frac{2 \pm \sqrt{(-2)^2 - 4 \cdot 1 \cdot (-15)}}{2} = \frac{2 \pm \sqrt{4 + 60}}{2} = \frac{2 \pm \sqrt{64}}{2} = \frac{2 \pm 8}{2}$$ - Solutions: $$x_1 = \frac{2 + 8}{2} = 5$$ $$x_2 = \frac{2 - 8}{2} = -3$$ 7. **Select valid solution:** - Since the graph shows $x > 0$, choose $x = 5$. 8. **Find $y$ coordinate:** - Substitute $x = 5$ into $g(x)$: $$y = 5 - 2 = 3$$ 9. **Final answer:** - The coordinates of point $B$ are $(5, 3)$.