Solution:

From the problem and the graph provided:

1. Identifying the components of the equation:

   • The graph represents the total cost $C$ of renting a truck in terms of the number of miles $m$ driven.
   • The equation is in the form of a linear function: $C = am + b$ where:
     • $a$ is the slope (the cost per mile),
     • $b$ is the y-intercept (the initial fixed charge when $m = 0$).

2. Finding the y-intercept $b$:

   • From the graph, the cost when $m = 0$ is approximately $40. Thus: $b = 40$

3. Finding the slope $a$:

   • The slope is calculated as: $a = \frac{\Delta C}{\Delta m} = \frac{\text{Change in cost}}{\text{Change in miles}}$
   • Using two points from the graph:
     • Point 1: $(0, 40)$
     • Point 2: $(10, 70)$
   • Compute: $a = \frac{70 - 40}{10 - 0} = \frac{30}{10} = 3$
   • So, the slope $a = 3$, which means the cost increases by $3 for every mile driven.

4. Writing the equation:

   • Substituting $a = 3$ and $b = 40$ into the equation: $C = 3m + 40$

Slope Interpretation:

• The slope of the graph, $a = 3$, represents the cost per mile. For every additional mile driven, the total cost increases by $3.

Context of the Problem:

• The initial cost of renting the truck is $40 (even if no miles are driven).
• For each mile driven, an additional $3 is added to the total cost.

Let me know if you'd like further explanation or examples! Below are some related questions for practice.

Related Questions:

1. If Colton drives 15 miles, what will be the total cost of the rental?
2. How many miles can Colton drive if he has a budget of $100 for the rental?
3. What would happen to the graph if the cost per mile increased to $5?
4. What does the y-intercept represent in this context, and why is it significant?
5. How would you verify the equation $C = 3m + 40$ using additional points on the graph?

Tip:

When analyzing linear equations, always start by identifying the slope (rate of change) and the y-intercept (starting value). These will help you form and interpret the equation effectively!