Let's go through the questions from the image and work through them:

5. Find the slope and interpret its meaning.

To find the slope of the line, we use the formula:

$\text{slope} = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}$

From the graph, you can select two points. Let's use the points (0, 15) and (3, 21).

• $x_1 = 0$, $y_1 = 15$
• $x_2 = 3$, $y_2 = 21$

$\text{slope} = \frac{21 - 15}{3 - 0} = \frac{6}{3} = 2$

Interpretation: The slope represents the additional cost per game. In this case, it means that for every game played, the total cost increases by $2.

6. Find the y-intercept and interpret its meaning.

The y-intercept is the point where the line crosses the y-axis, which is where $x = 0$.

From the graph, we can see that when $x = 0$, $y = 15$. So, the y-intercept is 15.

Interpretation: The y-intercept represents the initial fixed cost, which in this context is the entrance fee. This means the family pays $15 to enter the arcade before playing any games.

7. Write an equation to represent the relationship between $x$ (the number of games) and $y$ (the total cost).

The general form of the equation of a line is:

$y = mx + b$

Where:

• $m$ is the slope (which we found to be 2),
• $b$ is the y-intercept (which is 15).

Thus, the equation is:

$y = 2x + 15$

This equation represents the total cost $y$ in terms of the number of games $x$.

Do you want more details or have any questions about this?

Here are five related questions to expand on the concepts:

1. How would the equation change if the entrance fee increased to $20?
2. What would happen to the slope if each game cost $3 instead of $2?
3. How can you determine the number of games played if you know the total cost?
4. What is the total cost if the family plays 10 games?
5. Can you identify another point on the graph to confirm the equation?

Tip: Always check your graph and points used for slope calculation to ensure accuracy in real-world contexts.