B2. Write the equation of a line with a positive slope that forms a right-angled triangle with the coordinate axes, having an area of 9 square units, and intersects the abscissa at $x=-3$, in explicit, implicit, and segment form.
B2. The intercepts with the coordinate axes form a right-angled triangle, whose area we calculate as half the product of the legs $p=\frac{k_{1} \cdot k_{2}}{2}$. From the problem, it is clear that the length of one leg is 3, and the length of the other leg is calculated using the area, resulting in 6. Since the slope of the line is positive, the line intersects the coordinate axes at the points $(-3,0)$ and $(0,6)$. Using these two points, we can write all three forms of the equation of the line. The intercept form is $\frac{x}{-3}+\frac{y}{6}=1$, the implicit form is $-2 x+y-6=0$, and the explicit form is $y=2 x+6$.
Identifying that the triangle is right-angled ..... 1 point
Writing or using the formula for the area of a right-angled triangle $p=\frac{k_{1} \cdot k_{2}}{2}$ ..... 1 point
Writing or using that the length of one leg is 3 units ..... 1 point
Calculating the other leg as 6 units ..... 1 point
Writing or using the points $(-3,0)$ and $(0,6)$ ..... 1 point
Intercept form $\frac{x}{-3}+\frac{y}{6}=1$ ..... 1 point
Implicit form $-2 x+y-6=0$ ..... 1 point
Explicit form $y=2 x+6$ ..... 1 point