Let's solve the question using the given graph.

1. Equation of the Line:

   • The graph gives one point on the line: $(10, 2)$. This means that when the cost of the meal (x) is $10, the tip (y) is $2.
   • To find the equation of the line, we need the slope (m) and the y-intercept (b) in the form $y = mx + b$.
   • The slope $m = \frac{\Delta y}{\Delta x}$, which is the rise over the run. Looking at the graph, as the cost increases from 0 to $10 (Δx = 10)$, the tip increases from $0 to $2 (Δy = 2)$. Therefore: $m = \frac{2}{10} = 0.2$
   • Since the line passes through the origin (0,0), the y-intercept $b = 0$.
   • So, the equation of the line is: $y = 0.2x$

2. Interpreting the Slope:

   • The slope represents how much the tip increases for every dollar spent on the meal. In this case, since the slope is 0.2, the tip increases by $0.20 for each additional dollar spent on the meal.
   • Thus, the correct interpretation is: "The tip increases $0.20 for each dollar spent on the meal."

Do you want more details, or do you have any questions?

Here are five related questions to expand your understanding:

1. What is the importance of the y-intercept in linear equations?
2. How would the equation change if the line had a different slope?
3. Can you explain how to find the slope if the line was steeper?
4. How does changing the cost of the meal impact the total tip using this equation?
5. What happens to the graph if we change the slope to 0.5 instead of 0.2?

Tip: The slope is a ratio that measures the relationship between two quantities—how much one variable changes when another changes.