1. **Problem Statement:** We want to graph the cost of travel by bus and car using the slope of a line and similar triangles to understand the break-even point where costs are equal. 2. **Define Variables:** Let $x$ be the distance in kilometers and $y$ be the cost in AED. 3. **Bus Cost Equation:** The bus cost is constant regardless of distance: $$y = 67$$ This is a horizontal line. 4. **Car Cost Equation:** The car cost increases linearly with distance. Using the slope formula: $$\text{slope} = \frac{\text{change in cost}}{\text{change in distance}} = 30$$ So the car cost line is: $$y = 30x$$ 5. **Using Similar Triangles to Understand Slope:** The slope $m=30$ means for every 1 km increase in distance (run), the cost (rise) increases by 30 AED. 6. **Break-even Point:** Set bus cost equal to car cost: $$67 = 30x$$ Solve for $x$: $$x = \frac{67}{30} \approx 2.23$$ 7. **Graph Description:** - The bus cost line is horizontal at $y=67$. - The car cost line starts at the origin $(0,0)$ and rises steeply with slope 30. - The lines intersect at approximately $(2.23, 67)$, the break-even point. This graph visually shows that for distances less than 2.23 km, car travel is cheaper, and beyond that, the bus is more cost-effective.